Trigonometry Examples

$\frac{\tan (x)}{\sin (x)} = \sec (x)$

Step 1

Start on the left side.

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

Step 2

Write $\tan (x)$ in sines and cosines using the quotient identity.

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Cancel the common factor of $\sin (x)$ .

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

Step 4

Rewrite $\frac{1}{\cos (x)}$ as $\sec (x)$ .

$\sec (x)$

Step 5

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

$\frac{\tan (x)}{\sin (x)} = \sec (x)$ is an identity