## Algebra 2 Common Core

$$\cot\theta=\sqrt {\frac{1}{\sin^{2}\theta}-1}$$
Start with the Pythagorean Identity $$\csc^{2}\theta=1+\cot^{2}\theta.$$ Rearrange terms and solve for $\cot\theta$: $$\cot^{2}\theta=\csc^{2}\theta-1$$ $$\cot\theta=\sqrt {\csc^{2}\theta-1}.$$ Using the Reciprocal Identity $$\sin\theta=\frac{1}{\csc\theta},$$ substitute to obtain $$\cot\theta=\sqrt {\frac{1}{\sin^{2}\theta}-1}.$$