Mathematics

Problem

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

\theta

. a. (i)

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

b. (ii) Prove that

S=2\csc\theta

. c. (iii) Using the simplified form, calculate

S

for

\theta=30^\circ