Algebra Examples

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

Step 1

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

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Step 1.1

Multiply by $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Rewrite $\sec (x)$ in terms of sines and cosines.

$\frac{1}{\cos (x)} \cos^{2} (x)$

Step 4

Cancel the common factor of $\cos (x)$ .

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Step 4.1

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

$\frac{1}{\cos (x)} (\cos (x) \cos (x))$

Step 4.2

Cancel the common factor.

$\frac{1}{\cos (x)} (\cos (x) \cos (x))$

Step 4.3

Rewrite the expression.

$\cos (x)$