#### Answer

$\cot\theta+\tan\theta=\sec\theta\csc\theta$

#### Work Step by Step

Start with the left side:
$\cot\theta+\tan\theta$
Rewrite in terms of sine and cosine:
$=\frac{\cos\theta}{\sin\theta}+\frac{\sin\theta}{\cos\theta}$
Get a common denominator:
$=\frac{\cos\theta}{\sin\theta}*\frac{\cos\theta}{\cos\theta}+\frac{\sin\theta}{\cos\theta}*\frac{\sin\theta}{\sin\theta}$
$=\frac{\cos^2\theta}{\sin\theta\cos\theta}+\frac{\sin^2\theta}{\sin\theta\cos\theta}$
$=\frac{\cos^2\theta+\sin^2\theta}{\sin\theta\cos\theta}$
Simplify:
$=\frac{1}{\sin\theta\cos\theta}$
$=\frac{1}{\cos\theta}*\frac{1}{\sin\theta}$
$=\sec\theta\csc\theta$
Since this equals the right side, the identity has been proven.