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

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

Step 1

Simplify with factoring out.

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

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

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

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

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Multiply $\tan^{2} (x)$ by $\tan^{2} (x)$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

$\tan^{4} (x)$