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

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

Simplify with factoring out.

Factor $\cos^{2} (x)$ out of $\cos^{2} (x) \sec^{2} (x)$ .

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

Factor $\cos^{2} (x)$ out of $- \cos^{2} (x)$ .

$\cos^{2} (x) (\sec^{2} (x)) + \cos^{2} (x) \cdot - 1$

Factor $\cos^{2} (x)$ out of $\cos^{2} (x) (\sec^{2} (x)) + \cos^{2} (x) \cdot - 1$ .

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

Apply pythagorean identity.

$\cos^{2} (x) \tan^{2} (x)$

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

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

Apply the product rule to $\frac{\sin (x)}{\cos (x)}$ .

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

Cancel the common factor of $\cos^{2} (x)$ .

Cancel the common factor.

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

Rewrite the expression.

$\sin^{2} (x)$