The principal value of $\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)$
Answer & explanation
Correct answer: option 4
$\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)=\pi-\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
as $\cot^{-1}(-x)$
$\pi - \cot^{-1}(x)$
$=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$