#### Answer

$\frac{\cot\theta}{\csc\theta}=\cos\theta$

#### Work Step by Step

Start with the left side:
$\frac{\cot\theta}{\csc\theta}$
Rewrite in terms of sine and cosine:
$=\frac{\frac{\cos\theta}{\sin\theta}}{\frac{1}{\sin \theta}}$
Multiply top and bottom by $\sin\theta$ and simplify:
$=\frac{\frac{\cos\theta}{\sin\theta}*\sin\theta}{\frac{1}{\sin \theta}*\sin\theta}$
$=\frac{\cos\theta}{1}$
$=\cos \theta$
Since this equals the right side, the identity has been proven.