Simplify (cot(x))/(csc(x))

$\frac{\cot (x)}{\csc (x)}$

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

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

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

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

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

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

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

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

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

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Cancel the common factor.

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

Rewrite the expression.

$\cos (x)$

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