Prove the following identity for every acute angle :

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Prove the following identity for every acute angle

\theta

: (i) Rewrite each trigonometric function in

\sin(90^{\circ}-\theta)\sec\theta + \cos(90^{\circ}-\theta)\csc\theta

solely in terms of

\sin\theta

and

\cos\theta

. (ii) Simplify the resulting expression step by step to show that it equals

2