#### Answer

$\tan \frac{\theta}{2}=\csc \theta-\cot \theta$

#### Work Step by Step

Start with the right side:
$\csc\theta-\cot\theta$
Write everything in terms of sine and cosine:
$=\frac{1}{\sin\theta}-\frac{\cos\theta}{\sin\theta}$
$=\frac{1-\cos \theta}{\sin\theta}$
Use the identity $\tan \frac{\theta}{2}=\frac{1-\cos \theta}{\sin\theta}$:
$=\tan \frac{\theta}{2}$
Since this equals the left side, the identity has been proven.