Trigonometry Question

Trigonometry Test

There will be 25 questions and timing will be 2 hour.

1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
Determine:
(i) sin A, cos A
(ii) sin C, cos C
2. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.
3. If 3 cot A = 4, check whether (1 – tan²A)/(1 + tan²A) = cos² A – sin²A or not.
4. In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
5. Show that :
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° cos 52° – sin 38° sin 52° = 0
6. Prove the identities:
(i) √[1 + sinA/1 – sinA] = sec A + tan A
(ii) (1 + tan²A/1 + cot²A) = (1 – tan A/1 – cot A)² = tan²A
7. If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1.
8. Prove that (sin A – 2 sin³A)/(2 cos³A – cos A) = tan A.
9. Prove that (1 – cos² A) cosec²A = 1
10. Prove that (sec²θ − 1)(cosec²θ − 1) = 1
11. Prove that (1 – sin θ) / (1 + sin θ) = (sec θ – tan θ)²
12. Prove that tan²θ − sin² θ = tan² θ sin² θ
13. Prove that : (1 + tan² θ)(1 – sin θ)(1 + sin θ) = 1
14. Prove that cosec⁶ θ = cot⁶ θ + 3cot² θ cosec² θ + 1
15. If sin θ = 1/√2, find all other trigonometric ratios of angle θ.