## Algebra 2 Common Core

$$cot\theta=\pm\sqrt{csc^{2}\theta-1}$$
By identity, $csc^{2}\theta=1+cot^{2}\theta$. Subtracting 1 from both sides $csc^{2}{\theta}-1=\cot^{2}{\theta} \\\cot^{2}{\theta}=\csc^{2}{\theta}-1$ Taking square-root on both sides, $$\cot\theta=\pm\sqrt{\csc^{2}\theta-1}$$