## Precalculus (6th Edition)

$\frac{\cot\theta}{\csc\theta}=\cos\theta$
Start with the left side: $\frac{\cot\theta}{\csc\theta}$ Rewrite in terms of sine and cosine: $=\frac{\frac{\cos\theta}{\sin\theta}}{\frac{1}{\sin \theta}}$ Multiply top and bottom by $\sin\theta$ and simplify: $=\frac{\frac{\cos\theta}{\sin\theta}*\sin\theta}{\frac{1}{\sin \theta}*\sin\theta}$ $=\frac{\cos\theta}{1}$ $=\cos \theta$ Since this equals the right side, the identity has been proven.