Browse Questions

# Solve the following for x $tan^{-1}x+2cot^{-1}x=\frac{2\pi}{3}$

Toolbox:
• $tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$
• $cot\frac{\pi}{6}=\sqrt3$
Given equation can be written as
$\large\:tan^{-1}x+cot^{-1}x+cot^{-1}x=\large\frac{2\pi}{3}$
We know that $tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$
$\Rightarrow\:\large\frac{\pi}{2}+cot^{-1}x=\large\frac{2\pi}{3}$
$\Rightarrow\:\large\:cot^{-1}x=\large\frac{2\pi}{3}-\large\frac{\pi}{2}=\large\frac{\pi}{6}$
$\Rightarrow\:\large\:x=\large\:cot\frac{\pi}{6}=\large\sqrt3$