Trigonometry Examples

$\frac{\tan (x)}{\sec (- x)}$

Step 1

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

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

Step 2

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

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

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (- x)}$ .

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

Step 4

Write $\cos (- x)$ as a fraction with denominator $1$ .

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

Step 5

Simplify.

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Step 5.1

Divide $\cos (- x)$ by $1$ .

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

Step 5.2

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

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

Step 6

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

$\tan (x) \cos (x)$

Step 7

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

$\sin (x)$