Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\tan (x)$

Step 5

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

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