## Algebra 2 Common Core

$$\sec^{2}\theta$$
Simplify $$\tan\theta(\cot\theta+\tan\theta)$$ Use the Reciprocal Identity $$\cot\theta= \frac{1}{\tan\theta}$$ to obtain $$\tan\theta\bigg(\frac{1}{\tan\theta}+\tan\theta\bigg)=1+\tan^{2}\theta.$$ Finally, use the Pythagorean Identity $$1+\tan^{2}\theta=\sec^{2}\theta$$ to obtain $$\tan\theta(\cot\theta+\tan\theta)=\sec^{2}\theta.$$