## Algebra 2 Common Core

$\cos^{2}\theta$
Step 1: By definition, $\tan\theta =\frac{\sin\theta}{\cos\theta}$ and $\cot\theta=\frac{\cos\theta}{\sin\theta}$ Hence, $\tan\theta\times \cot\theta-\sin^{2}\theta= \frac{\sin\theta}{\cos\theta}\times\frac{\cos\theta}{\sin\theta}-\sin^{2}\theta$ Step 2: Simplifying the expression gives, $\tan\theta\times \cot\theta-\sin^{2}\theta= 1-\sin^{2}\theta$ Step 3: By the identity $\sin^{2}\theta+\cos^{2}\theta=1$, replace $1-\sin^{2}\theta$ by $\cos^{2}\theta$ Hence, $\tan\theta\times \cot\theta-\sin^{2}\theta = \cos^{2}\theta$