Question Paper
Class / Subject: Class 10 (ICSE) · Mathematics
Chapter: Chapter 21 — Chapter 21: Trigonometric Identities
Time Allowed: 32 minutes
Max Marks: 16
1. What is the fundamental trigonometric identity? [1]
(A) sin²θ + cos²θ = 1
(B) sin θ + cos θ = 1
(C) sin²θ - cos²θ = 1
(D) sin θ × cos θ = 1
2. What theorem is the fundamental identity derived from? [1]
(A) The Pythagorean theorem
(B) Thales' theorem
(C) Euclid's theorem
(D) Newton's laws
3. What is another trigonometric identity? [1]
(A) 1 + tan²θ = sec²θ
(B) 1 + tan²θ = cos²θ
(C) 1 - tan²θ = sec²θ
(D) tan²θ = sec²θ - 2
4. What identity relates cot and cosec? [1]
(A) 1 + cot²θ = cosec²θ
(B) 1 - cot²θ = cosec²θ
(C) cot²θ = cosec²θ + 2
(D) cot θ = cosec θ
5. What do identities help simplify? [1]
(A) Complex trigonometric expressions
(B) Only simple numbers
(C) Nothing useful
(D) Only geometry problems
6. Why are identities useful? [1]
(A) To solve trigonometric equations efficiently
(B) To make equations harder
(C) No reason
(D) Only for tests
7. If sin θ = 0.6, what is cos²θ? [1]
(A) 0.64
(B) 0.36
(C) 1
(D) 0.6
8. Why study trigonometric identities? [1]
(A) Essential for advanced trigonometry
(B) No reason
(C) It's not useful
(D) Only for tests
9. What is the fundamental trigonometric identity? [1]
(A) sin²θ + cos²θ = 1
(B) sin θ + cos θ = 1
(C) sin²θ - cos²θ = 1
(D) sin θ × cos θ = 1
10. What theorem is the fundamental identity derived from? [1]
(A) The Pythagorean theorem
(B) Thales' theorem
(C) Euclid's theorem
(D) Newton's laws
11. What is another trigonometric identity? [1]
(A) 1 + tan²θ = sec²θ
(B) 1 + tan²θ = cos²θ
(C) 1 - tan²θ = sec²θ
(D) tan²θ = sec²θ - 2
12. What identity relates cot and cosec? [1]
(A) 1 + cot²θ = cosec²θ
(B) 1 - cot²θ = cosec²θ
(C) cot²θ = cosec²θ + 2
(D) cot θ = cosec θ
13. What do identities help simplify? [1]
(A) Complex trigonometric expressions
(B) Only simple numbers
(C) Nothing useful
(D) Only geometry problems
14. Why are identities useful? [1]
(A) To solve trigonometric equations efficiently
(B) To make equations harder
(C) No reason
(D) Only for tests
15. If sin θ = 0.6, what is cos²θ? [1]
(A) 0.64
(B) 0.36
(C) 1
(D) 0.6
16. Why study trigonometric identities? [1]
(A) Essential for advanced trigonometry
(B) No reason
(C) It's not useful
(D) Only for tests