# How do you prove  (csc+cot)(csc-cot)=1?

Oct 17, 2015

${\csc}^{2} \theta = 1 + {\cot}^{2} \theta$ is a trigonometric identity.

#### Explanation:

$\left[1\right] \textcolor{w h i t e}{X X} \left(\csc \theta + \cot \theta\right) \left(\csc \theta - \cot \theta\right) = 1$

Property: $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

$\left[2\right] \textcolor{w h i t e}{X X} {\csc}^{2} \theta - {\cot}^{2} \theta = 1$

$\left[3\right] \textcolor{w h i t e}{X X} {\csc}^{2} \theta = 1 + {\cot}^{2} \theta$

This is a trigonometric identity.