Evaluate (cot(theta))/(csc(theta))

$\frac{\cot (θ)}{\csc (θ)}$

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

$\frac{\cot (θ)}{\frac{1}{\sin (θ)}}$

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

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

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

$\frac{\cos (θ)}{\sin (θ)} \sin (θ)$

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$\cos (θ)$