Trigonometry Examples

$\tan (x) + \cos (- x) + \tan (- x)$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{\sin (x)}{\cos (x)} + \cos (- x) + \tan (- x)$

Step 1.2

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

$\frac{\sin (x)}{\cos (x)} + \cos (x) + \tan (- x)$

Step 1.3

Since $\tan (- x)$ is an odd function, rewrite $\tan (- x)$ as $- \tan (x)$ .

$\frac{\sin (x)}{\cos (x)} + \cos (x) - \tan (x)$

Step 1.4

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

$\frac{\sin (x)}{\cos (x)} + \cos (x) - \frac{\sin (x)}{\cos (x)}$

Step 2

Combine the opposite terms in $\frac{\sin (x)}{\cos (x)} + \cos (x) - \frac{\sin (x)}{\cos (x)}$ .

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Step 2.1

Subtract $\frac{\sin (x)}{\cos (x)}$ from $\frac{\sin (x)}{\cos (x)}$ .

$0 + \cos (x)$

Step 2.2

Add $0$ and $\cos (x)$ .

$\cos (x)$