Simplify (tan(x))/(sec(x)^2)

$\frac{\tan (x)}{\sec^{2} (x)}$

Factor $\sec (x)$ out of $\sec^{2} (x)$ .

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

Separate fractions.

$\frac{1}{\sec (x)} \cdot \frac{\tan (x)}{\sec (x)}$

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

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

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

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

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

$1 \cos (x) \sin (x)$

Multiply $\cos (x)$ by $1$ .

$\cos (x) \sin (x)$