Simplify 1/(sin(x)cot(x))

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

Step 1

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

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

Step 2

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

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

Step 3

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{\sin (x) \cos (x)}{\sin (x)}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

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

$\sec (x)$