Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Convert to sines and cosines.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

$\sin (x)$

Step 4

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

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