Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

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

Step 1.3

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

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 2

Apply pythagorean identity.

$\cos^{2} (x)$