The principal value of $\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is

The principal value of $\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is
  1. $\frac{2 \pi}{3}$
  2. $\frac{\pi}{3}$
  3. $\frac{-\pi}{3}$
  4. $\frac{\pi}{6}$

Solution

$\cot ^{-1}\left(\frac{-1}{\sqrt{3}}\right)=\pi-\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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