#### Answer

$\frac{\sin^2\theta}{\cos\theta}=\sec\theta-\cos\theta$

#### Work Step by Step

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