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

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

Step 1

Simplify with factoring out.

Reorder $\cos (x) \tan^{2} (x)$ and $- \cos (x) \sec^{2} (x)$ .

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

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

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

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

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

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

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

Step 2

Apply pythagorean identity.

$- \cos (x) \cdot 1$

Step 3

Multiply $- 1$ by $1$ .

$- \cos (x)$