8. INTRODUCTION TO TRIGONOMETRY

MAX MARKS: – 18

TIME- 1 H        

1. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

2. In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

3. Evaluate the following:

4. State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.

5. If tan (A + B) = √3 and tan (A – B) = 1/√3 ,0° < A + B ≤ 90°; A > B, find A and B.

6. Prove the following identities

(i) cos A/(1+sin A) + (1+sin A)/cos A = 2 sec A

(ii) tan θ/(1-cot θ) + cot θ/(1-tan θ) = 1 + sec θ cosec θ