Trigonometry CDS PYQ Topic Wise (2016

Q: How many Trigonometry questions come in CDS?

In the official papers we tagged: 30 in 2026, 32 in 2025, 25 in 2024, 27 in 2023, 29 in 2022, 30 in 2021, 30 in 2020, 16 in 2019, 20 in 2018, 22 in 2017 and 23 in 2016 (2 papers each year). That is 284 questions in all, about 13% of Elementary Mathematics.

Q: Which Trigonometry topics repeat in CDS?

Asked in the most papers: Trigonometric Identities, Trigonometric Ratios, Heights and Distances. The concept table lists every one with its count.

Q: Are these official CDS questions?

Yes. Every question is from an official CDS paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.

Explore: All CDS topics · CDS Elementary Mathematics PYQs · CDS hub · Syllabus & pattern · CDS 2026

Answer first

Trigonometry PYQs (previous year questions) for CDS: Trigonometry (Elementary Mathematics) had 284 questions across the 66 official CDS papers we tagged (2016–2026), and appeared in 22 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Trigonometric Identities, Trigonometric Ratios, Heights and Distances.

Year-wise question count

Asked in 11 of 11 years, with 2 papers each year.

Year	Questions
CDS 2026	30
CDS 2025	32
CDS 2024	25
CDS 2023	27
CDS 2022	29
CDS 2021	30
CDS 2020	30
CDS 2019	16
CDS 2018	20
CDS 2017	22
CDS 2016	23

Most-asked concepts

Sorted by the number of papers a concept appeared in.

Concept	Questions	Papers	Years
Trigonometric Identities	120	22	2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016
Trigonometric Ratios	68	22	2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016
Heights and Distances	42	20	2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016
Trigonometric Equations	23	13	2026, 2025, 2024, 2023, 2020, 2019, 2018, 2017, 2016
Maxima and Minima	12	7	2026, 2022, 2021, 2020
Maximum and Minimum	6	5	2024, 2023, 2018
Angle Measurement	5	4	2025, 2017
Circular Measure	5	3	2020, 2019
Complementary Angles	2	1	2016
Trigonometric Inequalities	1	1	2019

How to practise Trigonometry PYQs

Start with the concepts at the top of the table. They have come back the most.
Solve one year’s Trigonometry questions from the official PDF against the clock, then check the answer listed below.
Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.

CDS2026

Q.41 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of tan² + cot² from a given trigonometric equation PDF
Q.42 (CDS (I) Maths) · MCQ · Trigonometric Identities: Check which two trigonometric expressions are identities PDF
Q.43 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of 4 tan + 3 cot given 3 sin + 4 cos = 5 PDF
Q.44 (CDS (I) Maths) · MCQ · Heights and Distances: Height of a tower from two elevation tangents 70 m apart PDF
Q.45 (CDS (I) Maths) · MCQ · Heights and Distances: Distance between two observers on opposite sides of a tower PDF
Q.91 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of sin - cos given 12(tan + cot) = 25 PDF
Q.92 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of cosec + sec given 12(tan + cot) = 25 PDF
Q.93 (CDS (I) Maths) · MCQ · Trigonometric Identities: tan in terms of p and q from cosec - sin and sec - cos PDF
Q.94 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in p and q from cosec - sin and sec - cos PDF
Q.95 (CDS (I) Maths) · MCQ · Trigonometric Identities: sin² α in terms of p, q, m from a given relation PDF
Q.96 (CDS (I) Maths) · MCQ · Trigonometric Identities: Related ratio of β in terms of p, q, n from a given relation PDF
Q.97 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of p² + q² from a ratio involving cot PDF
Q.98 (CDS (I) Maths) · MCQ · Trigonometric Identities: tan in terms of p and q from the same ratio PDF
Q.99 (CDS (I) Maths) · MCQ · Trigonometric Identities: Relation between p and q defined by trigonometric fractions PDF
Q.100 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in p and q defined by trigonometric fractions PDF
Q.36 (CDS (II) Maths) · MCQ · Trigonometric Equations: Angle θ satisfying tan 6θ tan 3θ = 1 PDF
Q.37 (CDS (II) Maths) · MCQ · Trigonometric Equations: Value of sin x + cos x from a given tan equation PDF
Q.38 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of an expression given cos² x + cos⁴ x = 1 PDF
Q.39 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of sin x cos x given sin⁴ x + cos⁴ x = 1 PDF
Q.40 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of 4 cos θ + 3 sin θ given 3 cos θ + 4 sin θ = 4 PDF
Q.41 (CDS (II) Maths) · MCQ · Trigonometric Identities: Expression in m and n from cot θ ± cos θ PDF
Q.42 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a cosec - cot expression in terms of p PDF
Q.43 (CDS (II) Maths) · MCQ · Trigonometric Equations: Value of sin θ from a linear sin-cos equation PDF
Q.44 (CDS (II) Maths) · MCQ · Heights and Distances: Height of a hill from elevations at two kilometre-stones PDF
Q.45 (CDS (II) Maths) · MCQ · Heights and Distances: Height of a tower from subtended angle and depression PDF
Q.46 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of tan θ + cot θ given 5 sin θ + 12 cos θ = 13 PDF
Q.47 (CDS (II) Maths) · MCQ · Maxima and Minima: Ratio of greatest to least value of a sin² expression PDF
Q.48 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Statements on sin and tan products when angle C is obtuse PDF
Q.49 (CDS (II) Maths) · MCQ · Trigonometric Identities: sin 35° cos 35° in terms of p = cos 35° + cos 55° PDF
Q.50 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of p - q - pq for sec + tan and cosec - cot PDF

CDS2025

Q.21 (CDS (I) Maths) · MCQ · Trigonometric Equations: Find sin 2α + cos 2α given a quartic sine-cosine equation PDF
Q.22 (CDS (I) Maths) · MCQ · Trigonometric Identities: Which given sine-cosine power relations are identities PDF
Q.23 (CDS (I) Maths) · MCQ · Trigonometric Identities: Evaluate p^2 - 2pq with p = 1/(cosec + cot), q = cosec PDF
Q.24 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Sign of cosec - sec and tan - cot in the first quadrant PDF
Q.25 (CDS (I) Maths) · MCQ · Heights and Distances: Height of a tower from angle subtended and depression from above PDF
Q.26 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify sinθ/(1 - cotθ) + cosθ/(1 - tanθ) PDF
Q.27 (CDS (I) Maths) · MCQ · Angle Measurement: Angle subtended at centre by an arc of given length PDF
Q.28 (CDS (I) Maths) · MCQ · Trigonometric Equations: Value of sin θ + cos 2θ from a quadratic in cot θ PDF
Q.29 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Which trigonometric equations are possible PDF
Q.30 (CDS (I) Maths) · MCQ · Trigonometric Identities: Evaluate an expression given m^2(sinθ-1) + n^2(sinθ+1) = 0 PDF
Q.31 (CDS (I) Maths) · MCQ · Trigonometric Identities: Find sin^3 α - cos^3 α given sin α + cos α = √2 PDF
Q.32 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify (1 + cot - cosec)(1 + tan + sec) PDF
Q.33 (CDS (I) Maths) · MCQ · Trigonometric Identities: Find √2 sin θ given tan θ in terms of α PDF
Q.34 (CDS (I) Maths) · MCQ · Trigonometric Equations: Number of α for which a sine product becomes zero PDF
Q.35 (CDS (I) Maths) · MCQ · Trigonometric Equations: Solve tan 3x tan 6x = 1 for x below 30° PDF
Q.62 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Cosine of angle between room diagonal and floor diagonal PDF
Q.31 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Find sin θ when a nested radical equals cosec θ (official answer: D) PDF
Q.32 (CDS (II) Maths) · MCQ · Trigonometric Identities: Find cosec θ given 8 sin θ - cos θ = 4 (official answer: C) PDF
Q.33 (CDS (II) Maths) · MCQ · Trigonometric Identities: Find cot θ given 2 tan θ = sec^2 θ - 2 (official answer: A) PDF
Q.34 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify (sec θ - tan θ) minus a sine fraction (official answer: A) PDF
Q.35 (CDS (II) Maths) · MCQ · Trigonometric Identities: Evaluate a cosec/sec expression given cot θ = √7 (official answer: D) PDF
Q.36 (CDS (II) Maths) · MCQ · Angle Measurement: Acute angle of a right triangle given difference of angles in radians (official answer: C) PDF
Q.41 (CDS (II) Maths) · MCQ · Trigonometric Identities: Find (tan α / tan β)^2 from weighted sin/cos relations (official answer: C) PDF
Q.42 (CDS (II) Maths) · MCQ · Trigonometric Identities: Relation between m and n when α and β are complementary (official answer: D) PDF
Q.43 (CDS (II) Maths) · MCQ · Trigonometric Identities: Evaluate p sin θ + q cos θ given cosec - sin = p and sec - cos = q (official answer: C) PDF
Q.44 (CDS (II) Maths) · MCQ · Trigonometric Identities: Evaluate p^2q^2(p^2+q^2+3) from the same relations (official answer: B) PDF
Q.45 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Find tan^2 α from given sine and cosine ratios (official answer: A) PDF
Q.46 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Find tan^2 β from given sine and cosine ratios (official answer: C) PDF
Q.47 (CDS (II) Maths) · MCQ · Trigonometric Identities: Find sec θ given (1+sin θ)/cos θ in terms of p (official answer: B) PDF
Q.48 (CDS (II) Maths) · MCQ · Trigonometric Identities: Find tan θ given (1+sin θ)/cos θ in terms of p (official answer: A) PDF
Q.49 (CDS (II) Maths) · MCQ · Trigonometric Identities: Relation between p = sin+cos and q = sec+cosec (official answer: B) PDF
Q.50 (CDS (II) Maths) · MCQ · Trigonometric Identities: Express tan θ + cot θ in terms of p and q (official answer: B) PDF

CDS2024

Q.9 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Express cosec 79°(1 - cos 79°) in terms of t = cos 79° (official answer: D) PDF
Q.11 (CDS (I) Maths) · MCQ · Trigonometric Equations: Condition on p for x cos θ = x² + p to have a real root (official answer: B) PDF
Q.12 (CDS (I) Maths) · MCQ · Maximum and Minimum: Difference of greatest and least values of a trigonometric expression (official answer: C) PDF
Q.32 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of 5 sin θ - 3 cos θ given 3 sin θ + 5 cos θ = 5 (official answer: A) PDF
Q.34 (CDS (I) Maths) · MCQ · Maximum and Minimum: Minimum of a trigonometric expression in sin A (official answer: C) PDF
Q.51 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Acute angle from a tan-cot equation (official answer: C) PDF
Q.52 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of p + q from a trigonometric identity (official answer: C) PDF
Q.53 (CDS (I) Maths) · MCQ · Heights and Distances: Distance from a tower when elevation angles are complementary (official answer: A) PDF
Q.54 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Statements on sums of sines and cosines in a triangle (official answer: C) PDF
Q.77 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Sum of tangents of two angles in a square-triangle figure (official answer: D) PDF
Q.97 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Range of an angle in a figure of two touching circles in a rectangle (official answer: C) PDF
Q.11 (CDS (II) Maths) · MCQ · Maximum and Minimum: Maximum value of 8 sin θ - 4 sin² θ PDF
Q.12 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify an expression in tan α and tan β PDF
Q.13 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Sign of tan 50° - cot 50° and cot 25° - tan 25° PDF
Q.14 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of tan α cot 2β from tan(α+β) and tan(α-β) PDF
Q.15 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of sin²θ cos²θ (sec²θ + cosec²θ) PDF
Q.16 (CDS (II) Maths) · MCQ · Trigonometric Equations: Value of tan θ + cot θ from an exponential equation in sin θ PDF
Q.17 (CDS (II) Maths) · MCQ · Trigonometric Identities: Express cosec θ + sec θ given cosec θ - cot θ = m and sec θ - tan θ = n PDF
Q.18 (CDS (II) Maths) · MCQ · Heights and Distances: Width of a river from angles of depression from a bridge PDF
Q.35 (CDS (II) Maths) · MCQ · Trigonometric Ratios: cos θ of a triangle from its area and two sides PDF
Q.39 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a product of trigonometric expressions PDF
Q.40 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify (sin θ - 2 sin³θ)/(2 cos³θ - cos θ) PDF
Q.46 (CDS (II) Maths) · MCQ · Heights and Distances: Sum of elevation angles of a pole from two points PDF
Q.52 (CDS (II) Maths) · MCQ · Trigonometric Ratios: tan of angle ACP in a right triangle with a midpoint PDF
Q.56 (CDS (II) Maths) · MCQ · Trigonometric Ratios: sin θ + cos θ for a right triangle with given side relations PDF

CDS2023

Q.46 (CDS (I) Maths) · MCQ · Trigonometric Identities: Which given trigonometric equations are identities (official answer: B) PDF
Q.47 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of an expression given a value of sin θ (official answer: D) PDF
Q.48 (CDS (I) Maths) · MCQ · Trigonometric Identities: tan θ + cot θ in terms of m for a given power sum (official answer: C) PDF
Q.49 (CDS (I) Maths) · MCQ · Maximum and Minimum: Minimum value of 6 - 4 sin θ on a given range (official answer: B) PDF
Q.50 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of x satisfying an equation with standard angles (official answer: D) PDF
Q.51 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of an expression with complementary angles (official answer: D) PDF
Q.52 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of a difference of products of trig expressions (official answer: B) PDF
Q.53 (CDS (I) Maths) · MCQ · Trigonometric Equations: Angle satisfying a quadratic in cos and sin (official answer: A) PDF
Q.54 (CDS (I) Maths) · MCQ · Heights and Distances: Remaining time for a car to reach a tower from depression angles (official answer: B) PDF
Q.55 (CDS (I) Maths) · MCQ · Heights and Distances: Height of a tower seen from a ship's deck (official answer: C) PDF
Q.68 (CDS (I) Maths) · MCQ · Heights and Distances: cot of the angle at the top of a pole in a square field (official answer: C) PDF
Q.92 (CDS (I) Maths) · MCQ · Trigonometric Ratios: sin of angle ABD in a 6-8-10 triangle with altitude BD (official answer: C) PDF
Q.6 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Condition on a and b for a given sine expression to be possible (official answer: A) PDF
Q.23 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of 5 sin - 3 cos given 3 sin + 5 cos = 5 (official answer: B) PDF
Q.25 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a combination of powers of sin and cos (official answer: C) PDF
Q.26 (CDS (II) Maths) · MCQ · Trigonometric Equations: Value of sin + cos for a root of a cot quadratic (official answer: C) PDF
Q.27 (CDS (II) Maths) · MCQ · Trigonometric Equations: A value of theta satisfying tan 2θ tan 4θ = 1 (official answer: A) PDF
Q.28 (CDS (II) Maths) · MCQ · Trigonometric Identities: Expression equal to √2 sin x from a given relation (official answer: A) PDF
Q.29 (CDS (II) Maths) · MCQ · Trigonometric Equations: Number of solutions of a product of trig expressions (official answer: A) PDF
Q.30 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of x^2 + y^2 from two trig equations (official answer: B) PDF
Q.31 (CDS (II) Maths) · MCQ · Heights and Distances: Relation between heights of flagstaff and tower and angles (official answer: A) PDF
Q.32 (CDS (II) Maths) · MCQ · Heights and Distances: Distance advanced towards a tower with flagstaff in terms of H (official answer: C) PDF
Q.33 (CDS (II) Maths) · MCQ · Heights and Distances: Comparison of distances x and y with doubled elevation angle (official answer: B) PDF
Q.34 (CDS (II) Maths) · MCQ · Heights and Distances: Height of tower in terms of x and y with doubled elevation (official answer: D) PDF
Q.70 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Sum of powers of tan A given tan A + cot A = 2 (official answer: C) PDF
Q.71 (CDS (II) Maths) · MCQ · Trigonometric Identities: Which given trig equations are identities (official answer: C) PDF
Q.72 (CDS (II) Maths) · MCQ · Trigonometric Ratios: tan θ from an equation in sin and cos powers (official answer: D) PDF

CDS2022

Q.11 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of an expression with complementary angles (official answer: C) PDF
Q.46 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in x defined by trig ratio (official answer: B) PDF
Q.47 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of cot(2x - y) from given conditions (official answer: A) PDF
Q.48 (CDS (I) Maths) · MCQ · Maxima and Minima: Minimum of sin^4 + cos^4 - 2 sin^2 cos^2 (official answer: A) PDF
Q.49 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of cos^4 + sec^4 - 2 from a condition (official answer: C) PDF
Q.50 (CDS (I) Maths) · MCQ · Maxima and Minima: Range of cos^2 x + sec^2 x (official answer: D) PDF
Q.51 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Sum of acute angles from trig equations (official answer: C) PDF
Q.52 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of a sum of sines in a cyclic quadrilateral (official answer: A) PDF
Q.53 (CDS (I) Maths) · MCQ · Heights and Distances: Range of angle of elevation to an aeroplane (official answer: C) PDF
Q.54 (CDS (I) Maths) · MCQ · Heights and Distances: Relation between tower height and distance moved (official answer: C) PDF
Q.55 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in sec and tan (official answer: B) PDF
Q.56 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of 3 tan + 9 sec given tan + sec (official answer: C) PDF
Q.57 (CDS (I) Maths) · MCQ · Trigonometric Identities: Which given relations are identities (official answer: A) PDF
Q.59 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression from a tan-sec quadratic (official answer: A) PDF
Q.60 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of sin^4 + cos^4 from a condition (official answer: C) PDF
Q.43 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Sum of cos^2 of angles of a triangle (official answer: B) PDF
Q.44 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Sum of sin^2 of angles of a triangle (official answer: A) PDF
Q.46 (CDS (II) Maths) · MCQ · Heights and Distances: Angle of depression of a cloud's reflection (official answer: C) PDF
Q.47 (CDS (II) Maths) · MCQ · Heights and Distances: Distance from observer to the cloud (official answer: D) PDF
Q.51 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of sec + cosec + 2 from tan (official answer: B) PDF
Q.52 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a root expression from a linear trig equation (official answer: A) PDF
Q.54 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of an expression in x = (1 + sin)/cos (official answer: B) PDF
Q.55 (CDS (II) Maths) · MCQ · Trigonometric Identities: Which given relations are identities (official answer: A) PDF
Q.56 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of an expression from a sin-cos ratio (official answer: C) PDF
Q.57 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a difference of reciprocals in terms of x (official answer: A) PDF
Q.58 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a sixth and fourth power expression (official answer: A) PDF
Q.59 (CDS (II) Maths) · MCQ · Maxima and Minima: Minimum of 3600 sec^2 + 121 cosec^2 (official answer: D) PDF
Q.60 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify a square root of trig expressions (official answer: C) PDF
Q.68 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Ratio BC to AB from angle condition (official answer: B) PDF

CDS2021

Q.46 (CDS (I) Maths) · MCQ · Maxima and Minima: Least value of 3 sin^2 + 4 cos^2 (official answer: C) PDF
Q.47 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Range of sin cos product in first quadrant (official answer: B) PDF
Q.48 (CDS (I) Maths) · MCQ · Maxima and Minima: Statements on the range of sin^2 + cos^4 (official answer: D) PDF
Q.49 (CDS (I) Maths) · MCQ · Maxima and Minima: Ratio of greatest to smallest value of a trig expression (official answer: dropped in the final key) PDF
Q.50 (CDS (I) Maths) · MCQ · Trigonometric Identities: Condition for real solutions of an equation in sin (official answer: A) PDF
Q.51 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Compare given sine and cosine values (official answer: A) PDF
Q.52 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in sec-tan and cosec-cot (official answer: A) PDF
Q.53 (CDS (I) Maths) · MCQ · Trigonometric Identities: Cosec in terms of m when cosec - cot = m (official answer: D) PDF
Q.54 (CDS (I) Maths) · MCQ · Trigonometric Ratios: tan A + tan B in a right triangle (official answer: D) PDF
Q.55 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of cos 2a - cos 2b from given sums (official answer: A) PDF
Q.56 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of sin^2 from sec + cos (official answer: C) PDF
Q.57 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of a product of trig expressions (official answer: C) PDF
Q.58 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of k^2 from two tan-sec equations (official answer: D) PDF
Q.59 (CDS (I) Maths) · MCQ · Heights and Distances: Length of a leaning pole from equal subtended angles (official answer: dropped in the final key) PDF
Q.60 (CDS (I) Maths) · MCQ · Heights and Distances: Cot of angle a tower subtends at the farthest corner (official answer: C) PDF
Q.46 (CDS (II) Maths) · MCQ · Maxima and Minima: Minimum of cos^3 + sec^3 (official answer: C) PDF
Q.47 (CDS (II) Maths) · MCQ · Trigonometric Identities: tan + cot from a sin-cos equation (official answer: A) PDF
Q.48 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify a sum of cubic trig fractions (official answer: C) PDF
Q.49 (CDS (II) Maths) · MCQ · Heights and Distances: Height of a flagstaff using a ladder (official answer: B) PDF
Q.50 (CDS (II) Maths) · MCQ · Maxima and Minima: Maximum value of a trig expression (official answer: A) PDF
Q.51 (CDS (II) Maths) · MCQ · Heights and Distances: Angle range from depression to river banks (official answer: C) PDF
Q.52 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of sin^2 + cos from a given equation (official answer: A) PDF
Q.53 (CDS (II) Maths) · MCQ · Trigonometric Identities: Which given relations are identities (official answer: C) PDF
Q.54 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of an expression with complementary angles (official answer: A) PDF
Q.55 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of x^2 + y^2 + z^2 in polar-type form (official answer: C) PDF
Q.56 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of x^2 - y^2 with sec and tan (official answer: A) PDF
Q.57 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of an expression when tan = 1 (official answer: D) PDF
Q.58 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify a ratio of trig expressions (official answer: C) PDF
Q.59 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of an expression in triangle angles (official answer: A) PDF
Q.60 (CDS (II) Maths) · MCQ · Trigonometric Ratios: tan A + tan C in a right triangle (official answer: A) PDF

CDS2020

Q.51 (CDS (I) Maths) · MCQ · Circular Measure: Radians turned per second by a rotating wheel (official answer: C) PDF
Q.52 (CDS (I) Maths) · MCQ · Maxima and Minima: Least value of 25 cosec squared x plus sec squared x (official answer: B) PDF
Q.53 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Product of cotangents of multiples of an angle (official answer: A) PDF
Q.54 (CDS (I) Maths) · MCQ · Trigonometric Equations: Value of sec 4 theta when tan 6 theta equals cot 2 theta (official answer: A) PDF
Q.55 (CDS (I) Maths) · MCQ · Heights and Distances: Height at which a broken tree snapped (official answer: C) PDF
Q.56 (CDS (I) Maths) · MCQ · Heights and Distances: Height of a taller tower aligned with a pole and a shorter tower (official answer: A) PDF
Q.57 (CDS (I) Maths) · MCQ · Heights and Distances: Tower height from complementary elevation angles (official answer: B) PDF
Q.58 (CDS (I) Maths) · MCQ · Trigonometric Identities: Sum of squared sines of multiples of 6 degrees (official answer: D) PDF
Q.59 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify a sum of two trigonometric fractions (official answer: B) PDF
Q.60 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify a difference of trigonometric fractions (official answer: A) PDF
Q.61 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify an expression in tan and cot of x and y (official answer: A) PDF
Q.62 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify a square root of a sec-tan ratio (official answer: C) PDF
Q.63 (CDS (I) Maths) · MCQ · Trigonometric Ratios: sin plus cos when cot of a first-quadrant angle is given (official answer: C) PDF
Q.64 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of an expression in fourth powers of sin and cos (official answer: D) PDF
Q.65 (CDS (I) Maths) · MCQ · Trigonometric Ratios: sec plus cosec of the angle a rectangle's diagonal makes (official answer: A) PDF
Q.46 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of an expression in m and n from cosec-sin and sec-cos (official answer: B) PDF
Q.47 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of sin squared minus tan squared given cos plus sec (official answer: B) PDF
Q.48 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Trigonometric expression for angles of a triangle in a semicircle (official answer: D) PDF
Q.49 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Possible values of sine and cosine expressions in x (official answer: D) PDF
Q.50 (CDS (II) Maths) · MCQ · Circular Measure: Interior angle of a regular pentagon in radians (official answer: C) PDF
Q.51 (CDS (II) Maths) · MCQ · Circular Measure: Ratio of two angles from their difference and sum (official answer: B) PDF
Q.52 (CDS (II) Maths) · MCQ · Trigonometric Equations: Statements on a trig equation and tan plus cot (official answer: B) PDF
Q.53 (CDS (II) Maths) · MCQ · Circular Measure: Radius of a road curve turning through 42 degrees (official answer: A) PDF
Q.54 (CDS (II) Maths) · MCQ · Maxima and Minima: Maximum value of 3 sin theta minus 4 (official answer: B) PDF
Q.55 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a sine-cosine expression given their sum (official answer: D) PDF
Q.56 (CDS (II) Maths) · MCQ · Maxima and Minima: Least value of 9 sin squared plus 16 cos squared (official answer: B) PDF
Q.57 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of cos squared minus sin squared of 47 degrees (official answer: B) PDF
Q.58 (CDS (II) Maths) · MCQ · Trigonometric Identities: tan theta from cosec-sin and sec-cos expressions (official answer: B) PDF
Q.59 (CDS (II) Maths) · MCQ · Trigonometric Equations: Value of an expression when cos of a difference is 1 (official answer: B) PDF
Q.60 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Statements on values of trig expressions (official answer: A) PDF

CDS2019

Q.51 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Value of 2 sin x cos x when tan x is 1 (official answer: B) PDF
Q.52 (CDS (I) Maths) · MCQ · Trigonometric Identities: Evaluate a sum of sine-cosine products of complementary angles (official answer: C) PDF
Q.53 (CDS (I) Maths) · MCQ · Trigonometric Inequalities: Lower bound for an expression in sin theta (official answer: B) PDF
Q.54 (CDS (I) Maths) · MCQ · Heights and Distances: Ratio of tower heights at hexagon vertices from elevation angles (official answer: B) PDF
Q.55 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Product of tangents from 1 to 89 degrees (official answer: B) PDF
Q.56 (CDS (I) Maths) · MCQ · Heights and Distances: Distance between two parallel streets from turns and travel (official answer: C) PDF
Q.57 (CDS (I) Maths) · MCQ · Trigonometric Equations: Angle satisfying a relation between tan and cot (official answer: A) PDF
Q.58 (CDS (I) Maths) · MCQ · Trigonometric Identities: Sum of squared sines of complementary angles (official answer: B) PDF
Q.59 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of a sine-cosine power expression (official answer: A) PDF
Q.60 (CDS (I) Maths) · MCQ · Trigonometric Ratios: How many given trigonometric values are impossible (official answer: C) PDF
Q.28 (CDS (II) Maths) · MCQ · Circular Measure: Radian measure of a sector's angle from its area (official answer: B) PDF
Q.31 (CDS (II) Maths) · MCQ · Trigonometric Identities: Sum of logs of six trigonometric ratios (official answer: B) PDF
Q.32 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a sine power expression given a cosine equation (official answer: A) PDF
Q.33 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of a series in cot theta given sin theta (official answer: D) PDF
Q.34 (CDS (II) Maths) · MCQ · Heights and Distances: Relation between distances to two pillars with elevation angles (official answer: C) PDF
Q.35 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of an expression with complementary angles (official answer: C) PDF

CDS2018

Q.54 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify sin^4 minus cos^4 (official answer: D) PDF
Q.55 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Product of cotangents of complementary angles (official answer: B) PDF
Q.57 (CDS (I) Maths) · MCQ · Trigonometric Identities: Check two trigonometric identities (official answer: B) PDF
Q.58 (CDS (I) Maths) · MCQ · Heights and Distances: Tower height when square's side subtends 60 degrees (official answer: B) PDF
Q.59 (CDS (I) Maths) · MCQ · Heights and Distances: Extra height to climb so elevation and depression swap (official answer: B) PDF
Q.60 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of tan^n + cot^n when sec x cosec x = 2 (official answer: A) PDF
Q.61 (CDS (I) Maths) · MCQ · Trigonometric Identities: Value of sin^2+sin^4 when cos x+cos^2 x=1 (official answer: A) PDF
Q.62 (CDS (I) Maths) · MCQ · Trigonometric Identities: Relation between p and q for sinA+cosA and cubes (official answer: C) PDF
Q.63 (CDS (I) Maths) · MCQ · Maximum and Minimum: Range of a ratio of sec^2 and tan expressions (official answer: D) PDF
Q.64 (CDS (I) Maths) · MCQ · Trigonometric Ratios: tan C when hypotenuse is four times the altitude (official answer: A) PDF
Q.61 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of a tan expression given cos theta (official answer: B) PDF
Q.62 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Relation between angles when cos theta < cos phi (official answer: B) PDF
Q.63 (CDS (II) Maths) · MCQ · Heights and Distances: Ratio of flag height to dome radius from elevation angles (official answer: A) PDF
Q.64 (CDS (II) Maths) · MCQ · Trigonometric Ratios: tan(2A - B) from given sin(A+B) and cos B (official answer: C) PDF
Q.65 (CDS (II) Maths) · MCQ · Trigonometric Equations: Check two equations that give theta = 60 degrees (official answer: C) PDF
Q.66 (CDS (II) Maths) · MCQ · Trigonometric Identities: Conditions on p, q for given cos^2 and tan^2 values (official answer: C) PDF
Q.67 (CDS (II) Maths) · MCQ · Maximum and Minimum: Statements on bounds of cos+sec and sec^2+cosec^2 (official answer: C) PDF
Q.68 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of a cos power sum when sin^2 x + sin x = 1 (official answer: C) PDF
Q.69 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of (3cos - 5sin)^2 given 3sin + 5cos = 4 (official answer: D) PDF
Q.70 (CDS (II) Maths) · MCQ · Trigonometric Identities: Relation between m and n from two cot expressions (official answer: B) PDF

CDS2017

Q.59 (CDS (I) Maths) · MCQ · Angle Measurement: Relation between degrees and radians (official answer: A) PDF
Q.60 (CDS (I) Maths) · MCQ · Trigonometric Identities: Minimum of 9tan²θ+4cot²θ (official answer: C) PDF
Q.61 (CDS (I) Maths) · MCQ · Trigonometric Identities: Expression from x sinθ=y cosθ relation (official answer: B) PDF
Q.62 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Sum of sines when sum of cosines is 3 (official answer: A) PDF
Q.63 (CDS (I) Maths) · MCQ · Trigonometric Equations: θ satisfying cos θ + tan θ = 1 (official answer: A) PDF
Q.64 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify sin x times a root expression (official answer: A) PDF
Q.65 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify (cos⁴A-sin⁴A)/(cos²A-sin²A) (official answer: C) PDF
Q.66 (CDS (I) Maths) · MCQ · Trigonometric Equations: tan x from 7sin²x+3cos²x=4 (official answer: D) PDF
Q.67 (CDS (I) Maths) · MCQ · Heights and Distances: Height of lower plane from elevation angles (official answer: A) PDF
Q.68 (CDS (I) Maths) · MCQ · Trigonometric Identities: x²+y² for given trig expressions (official answer: C) PDF
Q.69 (CDS (I) Maths) · MCQ · Heights and Distances: Height of tree from depression angles (official answer: B) PDF
Q.80 (CDS (I) Maths) · MCQ · Heights and Distances: Ratio of pole heights at hexagon vertices (official answer: B) PDF
Q.100 (CDS (I) Maths) · MCQ · Heights and Distances: Height of plane above two milestones (official answer: B) PDF
Q.46 (CDS (II) Maths) · MCQ · Trigonometric Ratios: sin θ+cos θ for the acute angle of a 5-12-13 triangle (official answer: D) PDF
Q.47 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Range of sin x + cosec x (official answer: A) PDF
Q.48 (CDS (II) Maths) · MCQ · Trigonometric Ratios: cos θ given sin θ in m and n (official answer: A) PDF
Q.50 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Value of an expression with 45°, 30°, 60° (official answer: A) PDF
Q.51 (CDS (II) Maths) · MCQ · Angle Measurement: Angle between clock hands at 4:36 in radians (official answer: B) PDF
Q.52 (CDS (II) Maths) · MCQ · Trigonometric Identities: Count true statements on trig ranges (official answer: C) PDF
Q.53 (CDS (II) Maths) · MCQ · Heights and Distances: Statements on a building and a tower (official answer: C) PDF
Q.54 (CDS (II) Maths) · MCQ · Heights and Distances: Breadth of a river from bearings (official answer: C) PDF
Q.55 (CDS (II) Maths) · MCQ · Angle Measurement: Compare sin of 1 radian and 1 degree (official answer: B) PDF

CDS2016

Q.23 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Evaluate expression with cos 55° and sin 35° (official answer: C) PDF
Q.62 (CDS (I) Maths) · MCQ · Trigonometric Identities: Evaluate expression from given tan relations (official answer: D) PDF
Q.63 (CDS (I) Maths) · MCQ · Trigonometric Identities: Check two identities in cos and cosec (official answer: C) PDF
Q.64 (CDS (I) Maths) · MCQ · Trigonometric Identities: Simplify expression in p and q from cot, tan, sec (official answer: B) PDF
Q.65 (CDS (I) Maths) · MCQ · Heights and Distances: Ratio x/y from angles 30° and 45° (official answer: C) PDF
Q.66 (CDS (I) Maths) · MCQ · Trigonometric Equations: Solutions of an equation in cos θ (official answer: B) PDF
Q.67 (CDS (I) Maths) · MCQ · Trigonometric Ratios: Angle relation in a triangle (official answer: D) PDF
Q.68 (CDS (I) Maths) · MCQ · Trigonometric Equations: Range of a for an equation in tan²θ (official answer: C) PDF
Q.97 (CDS (I) Maths) · MCQ · Trigonometric Ratios: sin θ+cos θ given tan θ+cot θ (official answer: C) PDF
Q.71 (CDS (II) Maths) · MCQ · Trigonometric Identities: sin θ - cos θ from sin θ + cos θ (official answer: B) PDF
Q.72 (CDS (II) Maths) · MCQ · Trigonometric Identities: Value of cos-power expression given a relation (official answer: C) PDF
Q.73 (CDS (II) Maths) · MCQ · Heights and Distances: Distance a car moves as depression angle changes (official answer: B) PDF
Q.74 (CDS (II) Maths) · MCQ · Heights and Distances: Distance between two men either side of a tower (official answer: A) PDF
Q.75 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Evaluate cosec² and sec² expression (official answer: D) PDF
Q.76 (CDS (II) Maths) · MCQ · Trigonometric Identities: x²+4y² from trig relations (official answer: C) PDF
Q.77 (CDS (II) Maths) · MCQ · Trigonometric Identities: tan θ + cot θ from sin θ + cos θ (official answer: D) PDF
Q.78 (CDS (II) Maths) · MCQ · Trigonometric Identities: Range of sin⁴θ + cos⁴θ (official answer: B) PDF
Q.79 (CDS (II) Maths) · MCQ · Trigonometric Identities: Simplify expression in cot and cosec (official answer: A) PDF
Q.80 (CDS (II) Maths) · MCQ · Trigonometric Ratios: Compare ratios of 1 radian and 1° (official answer: D) PDF
Q.81 (CDS (II) Maths) · MCQ · Trigonometric Equations: Angle x from an equation in tan (official answer: C) PDF
Q.82 (CDS (II) Maths) · MCQ · Heights and Distances: Sun's altitude when shadow equals height (official answer: C) PDF
Q.83 (CDS (II) Maths) · MCQ · Complementary Angles: Statements on ratios of complementary angles (official answer: D) PDF
Q.85 (CDS (II) Maths) · MCQ · Complementary Angles: Product tan 1° ... tan 89° (official answer: B) PDF

FAQ

How many Trigonometry questions come in CDS?