Simplify (sec(x))/(sin(x))

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

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

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

Rewrite $\frac{\frac{1}{\cos (x)}}{\sin (x)}$ as a product.

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

Multiply $\frac{1}{\cos (x)}$ by $\frac{1}{\sin (x)}$ .

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

Separate fractions.

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

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x) \sec (x)$