Simplify sec(x)cos(x)-sin(x)^2

$\sec (x) \cos (x) - \sin^{2} (x)$

Rewrite in terms of sines and cosines, then cancel the common factors.

Rewrite $\sec (x) \cos (x)$ in terms of sines and cosines.

$\frac{1}{\cos (x)} \cos (x) - \sin^{2} (x)$

Cancel the common factors.

$1 - \sin^{2} (x)$

Apply pythagorean identity.

$\cos^{2} (x)$