Answer
$\frac{1-\sin^2\beta}{\cos\beta}=\cos\beta$
Work Step by Step
Start with the left side:
$\frac{1-\sin^2\beta}{\cos\beta}$
Simplify:
$=\frac{\cos^2\beta}{\cos\beta}$
$=\cos\beta$
Since this equals the right side, the identity has been proven.