> 
> Find the greatest real number $C$, such that the inequality $$|\tan x-\tan y|\geq C|x-y|$$ holds for all $$x,y \in \left(\frac{-\pi}{2},\frac{\pi}{2}\right)$$
> 
> 
> 

All I've done so far is rearranged the inequality $$\bigg|\frac{\tan x-\tan y}{x-y}\bigg| \geq C$$
So since I want this to work for any $x,y$ in the interval I want to minimize $$\bigg|\frac{\tan x-\tan y}{x-y}\bigg|$$ On the interval $\left(\frac{-\pi}{2},\frac{\pi}{2}\right)$ and let that equal $C$. Now this is where I'm drawing a blank.