Trigonometry Examples

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

Step 1

Start on the right side.

$\frac{\sec (x)}{\csc (x)}$

Step 2

Convert to sines and cosines.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

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

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.

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