Answer
$$\sin\theta$$
Work Step by Step
Simplify
$$\csc\theta-\cos\theta\cot\theta.$$
Use the Reciprocal Identity
$$\csc\theta=\frac{1}{\sin\theta}$$
and the Cotangent Identity
$$\cot\theta=\frac{\cos\theta}{\sin\theta}$$
to obtain
$$\csc\theta-\cos\theta\cot\theta=\bigg(\frac{1}{\sin\theta}\bigg)-\cos\theta\bigg(\frac{\cos\theta}{\sin\theta}\bigg)$$
$$=\frac{1-\cos^{2}\theta}{\sin\theta}.$$
Use the Pythagorean Identity
$$\sin^{2}\theta+\cos^{2}\theta=1$$
rearranged as
$$1-\cos^{2}\theta=\sin^{2}\theta$$
to produce
$$\csc\theta-\cos\theta\cot\theta=\frac{\sin^{2}\theta}{\sin\theta}=\sin\theta.$$
