# How do you simplify the expression cot^2x/(cscx+1)?

Sep 21, 2016

$\csc x - 1$

#### Explanation:

${\cot}^{2} \frac{x}{\csc x + 1}$

One of the Pythagorean identities is $1 + {\cot}^{2} x = {\csc}^{2}$

Rearranging:
${\cot}^{2} x = {\csc}^{2} x - 1$

Substitute ${\csc}^{2} x - 1$ into the numerator for ${\cot}^{2} x$

$\frac{{\csc}^{2} x - 1}{\csc x + 1}$

Factor the numerator by difference of squares:

$\frac{\left(\csc x + 1\right) \left(\csc x - 1\right)}{\csc x + 1}$

Cancel the common factor in numerator and denominator:

$\csc x - 1$