Answer
$\sec^4x-\sec^2x=\tan^4x+\tan^2x$
Work Step by Step
Simplify the left side:
$\sec^4x-\sec^2x$
$=\sec^2x(\sec^2x-1)$
$=\sec^2x\tan^2x$
Simplify the right side:
$\tan^4x+\tan^2x$
$=\tan^2x(\tan^2x+1)$
$=\tan^2x\sec^2x$
$=\sec^2x\tan^2x$
Since the left side and the right side are both equal to $\sec^2x\tan^2x$, they are equal to each other, and the identity is proven.