Solve for $x$: $\csc^{100}x+\tan^{100}x=1$ 
Solve for $x$: $$\mathrm{csc}^{100}x+\tan^{100}x=1$$

I have tried it so many times but couldn't draw any conclusion. Please help.

According to the Mark Bennet comment: $$\csc x\ge 1 ,\,\,\,\,\,\forall x\in\mathbb{R}.$$ Therefore for real solutions of this trig equation, we need $\tan x=0$ and $\csc x=1.$ If such a solution exist, then$$\sin x=0=1$$ which is a contradiction. Therefore there are no such real $x.$
