CBSE Class 10 Mathematics (Standard) Chapter 8 Introduction to Trigonometry Important Questions 2027
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32 questions from Introduction to Trigonometry appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Trigonometry unit — 12 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 4.6 questions per paper (OR alternatives counted separately)
- 7 question patterns repeated across papers
Important topics in Introduction to Trigonometry
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Trigonometric identities (sin2 + cos2 = 1 family) and proving identities | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★★ |
| 2 | Values of trig ratios at 0, 30, 45, 60, 90 degrees | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Evaluating expressions using standard values | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| 4 | Trigonometric ratios from a right triangle | Board 2023Board 2026Sample 2025 | ★☆☆☆☆ |
Repeated questions from Introduction to Trigonometry
1. Evaluate numeric expression at standard angles
4×Board 2023Board 2024Board 2025Sample 20251/2 marks
Evaluate : tan2 60 deg / (sin2 60 deg + cos2 30 deg)
2. Solve linear trig equation for the angle
2×Board 2025Sample 20261 marks
If 2sin(5x) = sqrt(3), 0 <= x <= 90 degrees, then x is equal to (A) 10 deg (B) 12 deg (C) 20 deg (D) 50 deg
3. sec+tan and sec-tan are reciprocals
2×Board 2024Sample 20261 marks
If sec(theta) + tan(theta) = x, then sec(theta) - tan(theta) will be (A) x (B) x2 (C) 2/x (D) 1/x
4. sin + cos = sqrt(3): square and derive
2×Board 2023Sample 20262/3 marks
If sin(theta) + cos(theta) = sqrt(3), then prove that tan(theta) + cot(theta) = 1
5. Rationalising fraction identity via sec2-tan2 / cosec2-cot2 = 1
2×Board 2023Sample 20263 marks
Prove that (cosA - sinA + 1)/(cosA + sinA - 1) = cosecA + cotA
6. Evaluate (a sin + b cos)/(a sin - b cos) given tan
2×Board 2023Sample 20251 marks
If tan(theta) = 5/2 then (4 sin(theta) + cos(theta)) / (4 sin(theta) - cos(theta)) is equal to A) 11/9 B) 3/2 C) 9/11 D) 4
7. Prove tan/(1-cot) + cot/(1-tan) = 1 + sec.cosec
2×Board 2024Board 20253 marks
Prove that : tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + sec theta cosec theta
Introduction to Trigonometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 5 | 9 |
| Board 2024 | 5 | 9 |
| Board 2025 | 6 | 12 |
| Sample 2025 | 4 | 7 |
| Board 2026 | 6 | 12 |
| Sample 2026 | 6 | 11 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Introduction to Trigonometry
Board 2026 6 questions
If cos A = 4/5, then the value of tan A is : (A) 3/5 (B) 3/4 (C) 4/3 (D) 5/3
If 2 sin A = 1, then the value of tan A + cot A is : (A) sqrt(3) (B) 4/sqrt(3) (C) sqrt(3)/2 (D) 1
If tan(theta) + 1/tan(theta) = 2, find the value of tan2(theta) + 1/tan2(theta).
Prove that : sqrt((1 - sin(theta))/(1 + sin(theta))) = sec(theta) - tan(theta)
Prove that : sec3(theta)/(sec2(theta) - 1) + cosec3(theta)/(cosec2(theta) - 1) = sec(theta) . cosec(theta) (sec(theta) + cosec(theta))
If sec(alpha)/cosec(beta) = p and tan(alpha)/cosec(beta) = q, then prove that (p2 - q2) sec2(alpha) = p2.
Sample 2026 6 questions
If sec(theta) + tan(theta) = x, then sec(theta) - tan(theta) will be (A) x (B) x2 (C) 2/x (D) 1/x
If 2sin(5x) = sqrt(3), 0 <= x <= 90 degrees, then x is equal to (A) 10 deg (B) 12 deg (C) 20 deg (D) 50 deg
Assertion (A): If cosA + cos2 A = 1, then sin2 A + sin4 A = 1. Reason (R): sin2 A + cos2 A = 1. [Options: (A) Both A and R true, R correct explanation (B) Both true, R not correct explanation (C) A true, R false (D) A false, R true]
If sin(A+B) = 1 and cos(A-B) = sqrt(3)/2, 0 < A, B < 90 degrees, find the measure of angles A and B.
If sin(theta) + cos(theta) = sqrt(3), then prove that tan(theta) + cot(theta) = 1
Prove that (cosA - sinA + 1)/(cosA + sinA - 1) = cosecA + cotA
Board 2025 6 questions
If theta is an acute angle and 7 + 4 sin theta = 9, then the value of theta is : (A) 90 deg (B) 30 deg (C) 45 deg (D) 60 deg
The value of tan2 theta - (1/cos theta x sec theta) is : (A) 1 (B) 0 (C) -1 (D) 2
If x cos 60 deg + y cos 0 deg + sin 30 deg - cot 45 deg = 5, then find the value of x + 2y.
Evaluate : tan2 60 deg / (sin2 60 deg + cos2 30 deg)
Prove that : tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + sec theta cosec theta
Prove that : (sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin2 A - 1)
Sample 2025 4 questions
If tan(theta) = 5/2 then (4 sin(theta) + cos(theta)) / (4 sin(theta) - cos(theta)) is equal to A) 11/9 B) 3/2 C) 9/11 D) 4
If theta = 30 deg then the value of 3 tan(theta) is A) 1 B) 1/sqrt(3) C) 3/sqrt(3) D) not defined
Evaluate: (2 sin2(60 deg) - tan2(30 deg)) / sec2(45 deg)
If cos(theta) + sin(theta) = 1, then prove that cos(theta) - sin(theta) = +/- 1
Board 2024 5 questions
If sec(theta) - tan(theta) = m, then the value of sec(theta) + tan(theta) is: (a) 1 - 1/m (b) m2 - 1 (c) 1/m (d) -m
If cos(alpha + beta) = 0, then value of cos((alpha + beta)/2) is equal to: (a) 1/sqrt(2) (b) 1/2 (c) 0 (d) sqrt(2)
Evaluate: 2*sqrt(2) cos 45 sin 30 + 2*sqrt(3) cos 30
If A = 60 degrees and B = 30 degrees, verify that: sin(A + B) = sin A cos B + cos A sin B
Prove that: tan(theta)/(1 - cot(theta)) + cot(theta)/(1 - tan(theta)) = 1 + sec(theta) cosec(theta)
Board 2023 5 questions
If 2 tan A = 3, then the value of (4 sin A + 3 cos A)/(4 sin A - 3 cos A) is (A) 7/sqrt(13) (B) 1/sqrt(13) (C) 3 (D) does not exist
[3/4 tan2 30 - sec2 45 + sin2 60] is equal to (A) -1 (B) 5/6 (C) -3/2 (D) 1/6
If sin theta + cos theta = sqrt(3), then find the value of sin theta * cos theta.
If sin alpha = 1/sqrt(2) and cot beta = sqrt(3), then find the value of cosec alpha + cosec beta.
Prove that: (tan theta + sec theta - 1)/(tan theta - sec theta + 1) = (1 + sin theta)/cos theta
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 8 Introduction to Trigonometry?
By how often and how recently they were asked: Trigonometric identities (sin^2 + cos^2 = 1 family) and proving identities; Values of trig ratios at 0, 30, 45, 60, 90 degrees; Evaluating expressions using standard values.
How many marks does Introduction to Trigonometry carry in the CBSE Class 10 Mathematics (Standard) exam?
Introduction to Trigonometry is part of the Trigonometry unit, which carries 12 marks in the official syllabus. In the analysed papers it had about 4.6 questions per paper.
Do questions from Introduction to Trigonometry repeat in board exams?
Yes — 7 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.