# How do you prove that cos(theta)csc(theta)=cot (theta)?

The function $\csc \theta = \frac{1}{\sin} \theta$, and so:
$\cos \theta \csc \theta = \cos \theta \cdot \frac{1}{\sin} \theta = \cos \frac{\theta}{\sin} \theta = \frac{1}{\tan} \theta = \cot \theta$.