Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Convert to sines and cosines.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

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

Step 4

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

$\tan (a)$

Step 5

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

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