Precalculus Examples

$\sec (- x) \sin (x) = \tan (x)$

Step 1

Start on the left side.

$\sec (- x) \sin (x)$

Step 2

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

$\sec (x) \sin (x)$

Step 3

Apply the reciprocal identity to $\sec (x)$ .

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

Step 4

Combine $\frac{1}{\cos (x)}$ and $\sin (x)$ .

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

Step 5

Rewrite $\frac{\sin (x)}{\cos (x)}$ as $\tan (x)$ .

$\tan (x)$

Step 6

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sec (- x) \sin (x) = \tan (x)$ is an identity