Algebra Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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.

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Step 3.1

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

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

Step 3.2

Add $2$ and $2$ .

$\tan^{4} (x)$