Evaluate (tan(x))/(sec(x))

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

Step 1

Rewrite $\sec (x)$ in terms of sines and cosines.

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

Step 2

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

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

Step 4

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 5

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

Cancel the common factor.

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

Rewrite the expression.

$\sin (x)$