Find the principal value of ^ -1 (3) - Vidyadip

MCQ

Find the principal value of $\cot ^{-1}(\sqrt{3})$

A
$\frac{2\pi}{3}$
✓
$\frac{\pi}{6}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{3}$

✓

Answer

Correct option: B.

$\frac{\pi}{6}$

b
Let $\cot ^{-1}(\sqrt{3})=y .$ Then cot $y=\sqrt{3}=\cot \left(\frac{\pi}{6}\right)$

We know that the range of the principal value branch of $\cot ^{-1}$ is $(0, \pi)$ and $\cot \left(\frac{\pi}{6}\right)=\sqrt{3}$

Therefore, the principal value of $\cot ^{-1}(\sqrt{3})$ is $\frac{\pi}{6}$

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