# Math Help - help

1. ## help

prove |x-y|>= |sin x - sin y|

2. For $x=y,$ there's nothing to prove.

Assume $x\ne y$ and by the MVT applied to $f(t)=\sin t,\,\exists\,\varphi\in(x,y)$ then, $\frac{\sin x-\sin y}{x-y}=\cos \varphi \implies \left| \sin x-\sin y \right|=\left| x-y \right|\left| \cos \varphi \right|.$

It remains a simple little step to solve this, I let you to figure out.