SSC CGL Trigonometry Verified Practice Test 2
15 structurally validated Trigonometry questions with unique options, mapped answers and explanations.
SSC CGL Trigonometry Verified Practice Test 2
15 structurally validated Trigonometry questions with unique options, mapped answers and explanations.
Preview all 15 questions in SSC CGL Trigonometry Verified Practice Test 2 (no login required)
- Identity
1. sec² θ - tan² θ is:
- A. 0
- B. 1 (Correct)
- C. sin² θ
- D. cos² θ
Explanation: From 1 + tan² θ = sec² θ, we get sec² θ - tan² θ = 1.
- Standard Angle
2. The value of sin 45° is:
- A. 1/2
- B. 1/√2 (Correct)
- C. √3/2
- D. 1
Explanation: sin 45° = 1/√2.
- Complementary Angle
3. tan 25° is equal to:
- A. cot 25°
- B. cot 65° (Correct)
- C. sec 65°
- D. sin 65°
Explanation: tan θ = cot (90° - θ).
- Ratio
4. If tan A = 5/12, then sin A is:
- A. 5/13 (Correct)
- B. 12/13
- C. 13/5
- D. 5/12
Explanation: Using a 5-12-13 triangle, sin A = 5/13.
- Standard Angle
5. The value of cos 30° is:
- A. 1/2
- B. √3/2 (Correct)
- C. 1/√3
- D. 1
Explanation: cos 30° = √3/2.
- Identity
6. cosec² A - cot² A is:
- A. 0
- B. 1 (Correct)
- C. sec² A
- D. sin² A
Explanation: From 1 + cot² A = cosec² A.
- Heights and Distances
7. If a ladder makes an angle of 60° with the ground and its length is 10 m, the height reached is:
- A. 5 m
- B. 5√3 m (Correct)
- C. 10/√3 m
- D. 10 m
Explanation: Height = 10 × sin 60° = 5√3 m.
- Standard Angle
8. The value of tan 60° is:
- A. 1/√3
- B. 1
- C. √3 (Correct)
- D. 2
Explanation: tan 60° = √3.
- Ratio
9. If sin A = 8/17, then cot A is:
- A. 8/15
- B. 15/8 (Correct)
- C. 17/8
- D. 15/17
Explanation: Using an 8-15-17 triangle, cot A = 15/8.
- Identity
10. If sin A = 1/2 and A is acute, then cos A equals:
- A. √3/2 (Correct)
- B. 1/2
- C. 1/√2
- D. 2/√3
Explanation: For an acute angle with sin A = 1/2, cos A = √3/2.
- Complementary Angle
11. sec 35° is equal to:
- A. cosec 55° (Correct)
- B. sin 55°
- C. tan 55°
- D. cot 35°
Explanation: sec θ = cosec (90° - θ).
- Standard Angle
12. The value of cos 90° is:
- A. 0 (Correct)
- B. 1/2
- C. 1
- D. Undefined
Explanation: cos 90° = 0.
- Heights and Distances
13. The angle of elevation of the top of a tower from a point 20 m away is 45°. The height of the tower is:
- A. 10 m
- B. 20 m (Correct)
- C. 20√2 m
- D. 40 m
Explanation: tan 45° = height / 20 = 1, so height = 20 m.
- Identity
14. If tan A = 3/4, then sin A × cos A equals:
- A. 3/25
- B. 12/25 (Correct)
- C. 7/25
- D. 24/25
Explanation: sin A = 3/5 and cos A = 4/5, so product = 12/25.
- Ratio
15. If cos A = 3/5, then sin A is:
- A. 4/5 (Correct)
- B. 3/4
- C. 5/4
- D. 2/5
Explanation: Using a 3-4-5 triangle, sin A = 4/5.