# How to verify the following identity?

## $\frac{\cos x - \cos y}{\sin x + \sin y} + \frac{\sin x - \sin y}{\cos x + \cos y} = 0$

Jul 17, 2018

 {(cosx-cosy)(cosx+cosy)+(sinx-siny)(sinx+siny)}/{(sinx+siny)*(cosx+cosy)

(1-cos^2y-sin^2y)/{(sinx+siny)(cosx+cosy)

(sin^2y-sin^2y)/{(sinx+siny)(cosx+cosy)

$\textcolor{red}{\text{The numerator becomes 0 and anything divided upon 0 is 0}}$

Hope you can understand it!!