Simplify the following expression completely and express your answer in terms of a…

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

Problem

Simplify the following expression completely and express your answer in terms of a single trigonometric function of

\theta

. (i)

S=\dfrac{\sin\theta}{1+\cos\theta}+\dfrac{1+\cos\theta}{\sin\theta}

(ii) Prove that

S=2\csc\theta

. (iii) Using the simplified form, calculate

S

for

\theta=30^\circ