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

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

Step 1

Simplify with factoring out.

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

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

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

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

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

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

Step 2

Apply pythagorean identity.

$\sin (x) \cdot 1$

Step 3

Multiply $\sin (x)$ by $1$ .

$\sin (x)$