Question

Find maxima and minima of $\tan x+\cot x$.

Answer 1

$A.M.\ge G.M.\Rightarrow \frac{\tan x+\cot x}{2}\ge \sqrt{\tan x\times \cot x}\Rightarrow \tan x+\cot x\ge 2$

So the minimum value will be $2$

and the maximum value will be infinite