Find the principal value of each of the following :
Question:

Find the principal value of each of the following :

$\tan ^{-1}(-\sqrt{3})$

Solution:

$\tan ^{-1}(-\sqrt{3})=-\tan ^{-1}(\sqrt{3})\left[\right.$ Formula: $\left.\tan ^{-1}(-x)=-\tan ^{-1}(x)\right]$

$=-\frac{\pi}{3}$