#### Answer

$\frac{\tan^2\alpha+1}{\sec\alpha}=\sec\alpha$

#### Work Step by Step

Start with the left side:
$\frac{\tan^2\alpha+1}{\sec\alpha}$
Use the identity $\tan^2\alpha+1=\sec^2\alpha$ to simplify:
$=\frac{\sec^2\alpha}{\sec\alpha}$
$=\sec\alpha$
Since this equals the right side, the identity has been proven.