# Write the value

Question:

Write the value of $\cos \left(\frac{\tan ^{-1} x+\cot ^{-1} x}{3}\right)$, when $x=-\frac{1}{\sqrt{3}}$

Solution:

$\cos \left(\frac{\tan ^{-1} x+\cot ^{-1} x}{3}\right)=\cos \left(\frac{\pi}{6}\right) \quad\left[\because \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right]$

$=\frac{\sqrt{3}}{2}$