# How do you simplify cot^2x(tan^2x+ 1)?

Mar 9, 2017

${\csc}^{2} x$

#### Explanation:

We start by factoring out a ${\cot}^{2} x$.

${\cot}^{2} x \left({\tan}^{2} x + 1\right)$

Use the identity ${\tan}^{2} x + 1 = {\sec}^{2} x$.

${\cot}^{2} x \left({\sec}^{2} x\right)$

Use $\sec x = \frac{1}{\cos} x$ and $\cot x = \cos \frac{x}{\sin} x$.

$\left({\cos}^{2} \frac{x}{\sin} ^ 2 x\right) \left(\frac{1}{\cos} ^ 2 x\right)$

$\frac{1}{\sin} ^ 2 x$

Use $\csc x = \frac{1}{\sin} x$.

${\csc}^{2} x$

Hopefully this helps!