CBSE Class 10 Mathematics (Basic) Chapter 8 Introduction to Trigonometry Important Questions 2027
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26 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 3.7 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 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Trigonometric ratios from a right triangle | Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| 4 | Evaluating expressions using standard values | Board 2023Board 2024Sample 2025 | ★☆☆☆☆ |
Repeated questions from Introduction to Trigonometry
1. Prove a trigonometric identity
7×Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 20263 marks
Prove that : (1 + cot2 A)/(1 + tan2 A) = ((1 – cot A)/(1 – tan A))2
2. Evaluate using Pythagorean identity constant
3×Board 2025Board 2026Sample 20261 marks
The value of (tan2 A – 1/cos2 A) is : (A) more than 1 (B) 1 (C) 0 (D) – 1
3. Find A and B from sum/difference equations
3×Board 2025Board 2026Sample 20252 marks
Find the values of A and B (0 ≤ A < 90°, 0 ≤ B < 90°), if tan (A + B) = 1 and tan (A – B) = 1/√3.
4. Evaluate expression using standard angle values
3×Board 2023Board 2024Sample 20251/2 marks
(1 − tan2 30°)/(1 + tan2 30°) is equal to (A) cos 60° (B) sin 60° (C) 1 (D) tan2 60°
5. Find one ratio given another
2×Board 2024Sample 20251 marks
If 3 cot A = 4, where 0° < A < 90°, then sec A is equal to (A) 5/4 (B) 4/3 (C) 5/3 (D) 3/4
6. Identify false standard-value statement
2×Board 2025Board 20261 marks
Which of the following statements is false ? (A) tan 45° = cot 45° (B) sin 90° = tan 45° (C) sin 30° = cos 30° (D) sin 45° = cos 45°
7. Prove tan 45 = 1 geometrically
2×Board 2025Board 20262 marks
Prove that tan 45° = 1 geometrically.
Introduction to Trigonometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 9 |
| Board 2024 | 4 | 7 |
| Board 2025 | 5 | 9 |
| Sample 2025 | 4 | 7 |
| Board 2026 | 5 | 9 |
| Sample 2026 | 4 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Introduction to Trigonometry
Board 2026 5 questions
Which of the following statements is false ? (A) tan 45° = cot 45° (B) sin 90° = tan 45° (C) sin 30° = cos 30° (D) sin 45° = cos 45°
The value of (tan2 A – 1/cos2 A) is : (A) more than 1 (B) 1 (C) 0 (D) – 1
Find the values of A and B (0 ≤ A < 90°, 0 ≤ B < 90°), if tan (A + B) = 1 and tan (A – B) = 1/√3.
Prove that tan 45° = 1 geometrically.
Prove that : (1 + cot2 A)/(1 + tan2 A) = ((1 – cot A)/(1 – tan A))2
Sample 2026 4 questions
Which one of the following is not equal to Unity?
A) sin2 x + cos2 x
B) cot2 x − cosec2 x
C) sec2 x − tan2 x
D) tan x . cot x
Evaluate : 2 sin30° tan60° − 3 cos2 60° sec2 30°
If sin x = 7/25, where x is an acute angle, then find the value of sin x . cos x (tan x + cot x).
Prove that : (sin x − cos x + 1) . (sec x − tan x) = (sin x + cos x − 1)
Board 2025 5 questions
Which of the following statements is false ? (A) tan 45° = cot 45° (B) sin 90° = tan 45° (C) sin 30° = cos 30° (D) sin 45° = cos 45°
The value of (tan2 A - 1/cos2 A) is : (A) more than 1 (B) 1 (C) 0 (D) -1
Find the values of A and B (0 ≤ A < 90°, 0 ≤ B < 90°), if tan (A + B) = 1 and tan (A - B) = 1/√3.
Prove that tan 45° = 1 geometrically.
Prove that : (1 + cot2 A)/(1 + tan2 A) = ((1 - cot A)/(1 - tan A))2
Sample 2025 4 questions
If 3 cot A = 4, where 0° < A < 90°, then sec A is equal to (A) 5/4 (B) 4/3 (C) 5/3 (D) 3/4
(1 − tan2 30°)/(1 + tan2 30°) is equal to (A) cos 60° (B) sin 60° (C) 1 (D) tan2 60°
If sin(A − B) = 1/2 and cos(A + B) = 1/2, 0° < A + B < 90° and A > B, then find the values of A and B.
Prove that: (cosec A − sin A)(sec A − cos A) = 1/(tan A + cot A).
Board 2024 4 questions
If sin θ = 1/3, then sec θ is equal to : (a) 2√2/3 (b) 3/(2√2) (c) 3 (d) 1/√3
For what value of θ, sin2 θ + sin θ + cos2 θ is equal to 2 ? (a) 45° (b) 0° (c) 90° (d) 30°
Evaluate: sin A cos B + cos A sin B; if A = 30° and B = 45°.
Prove that: (cot θ - cosec θ)2 = (1 - cos θ)/(1 + cos θ).
Board 2023 4 questions
If 2 cosθ = 1, then the value of θ is : (a) 45° (b) 60° (c) 30° (d) 90°
Evaluate : tan2 60° − 2 cosec2 30° − 2 tan2 30°.
Prove that secθ (1 − sinθ) (secθ + tanθ) = 1.
Prove that (1 + secθ)/secθ = sin2θ/(1 − cosθ).
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) 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; Trigonometric ratios from a right triangle.
How many marks does Introduction to Trigonometry carry in the CBSE Class 10 Mathematics (Basic) 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 3.7 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.