## Precalculus (6th Edition)

$\sec^4x-\sec^2x=\tan^4x+\tan^2x$
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.