The value of $2 \sin ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is

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

Solution

$2 \sin ^{-1}\left(\frac{1}{2}\right)+\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)=2 \times \frac{\pi}{6}+\frac{\pi}{3}=\frac{2 \pi}{3}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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