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