Prove that:`sqrt((1-costheta)/(1+costheta))={cosectheta-cottheta,if 0 < theta < pi`,if `pi < t<2pi` .

Explanation

To prove that

\[
\sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}} =
\begin{cases}
\csc \theta - \cot \theta & \text{if } 0 < \theta < \pi \\
-\csc \theta - \cot \theta & \text{if } \pi < \theta < 2\pi
\end{cases}
...