Answer
$\sin^2\alpha+\tan^2\alpha+\cos^2\alpha=\sec^2\alpha$
Work Step by Step
Start with the left side:
$\sin^2\alpha+\tan^2\alpha+\cos^2\alpha$
$=(\sin^2\alpha+\cos^2\alpha)+\tan^2\alpha$
$=1+\tan^2\alpha$
$=\sec^2\alpha$
Since this equals the right side, the identity has been proven.