Answer
$$\frac{\cot\theta}{\csc\theta}=\cos\theta$$
The identity is proved by simplifying the left side.
Work Step by Step
$$\frac{\cot\theta}{\csc\theta}=\cos\theta$$
Seeing that the left side is more complicated, we would simplify it, using the following identities $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ $$\csc\theta=\frac{1}{\sin\theta}$$
Therefore, the left side now would be $$\frac{\cot\theta}{\csc\theta}=\frac{\frac{\cos\theta}{\sin\theta}}{\frac{1}{\sin\theta}}$$ $$=\frac{\cos\theta\sin\theta}{\sin\theta}$$ $$=\cos\theta$$
The identity is hence proved.
