## Algebra 2 Common Core

$$\csc\theta$$
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 $$\sin\theta(1+\cot^{2}\theta)=\bigg(\frac{1}{\csc\theta}\bigg)\csc^{2}\theta=\csc\theta.$$