Precalculus Examples

$\sec^{3} (x) - \tan^{2} (x) \sec (x)$

Step 1

Factor $\sec (x)$ out of $\sec^{3} (x) - \tan^{2} (x) \sec (x)$ .

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Step 1.1

Factor $\sec (x)$ out of $\sec^{3} (x)$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

$\sec (x) \cdot 1$

Step 3

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

$\sec (x)$