Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Multiply $- \frac{\sin (x)}{\cos (x)} (- \sin (x))$ .

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Step 1.5.1

Multiply $- 1$ by $- 1$ .

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

Step 1.5.2

Multiply $\frac{\sin (x)}{\cos (x)}$ by $1$ .

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

Step 1.5.3

Combine $\frac{\sin (x)}{\cos (x)}$ and $\sin (x)$ .

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

Step 1.5.4

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.5.5

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.5.6

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

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

Step 1.5.7

Add $1$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

Separate fractions.

$\cos (x) + \frac{\sin (x)}{1} \cdot \frac{\sin (x)}{\cos (x)}$

Step 2.3

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\cos (x) + \frac{\sin (x)}{1} \tan (x)$

Step 2.4

Divide $\sin (x)$ by $1$ .

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