Find the principal value of cot ^{-1}left(fra | vedclass

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

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(B) Let $\cot ^{-1}\left(\frac{-1}{\sqrt{3}}ight) = y$. Then,$\cot y = \frac{-1}{\sqrt{3}}$.Since $\cot \left(\frac{\pi}{3}ight) = \frac{1}{\sqrt{3}}$,we have $\cot y = -\cot \left(\frac{\pi}{3}ight)$.Using the property $\cot(\pi - 	heta) = -\cot 	heta$,we get $\cot y = \cot \left(\pi - \frac{\pi}{3}ight) = \cot \left(\frac{2\pi}{3}ight)$.The range of the principal value branch of $\cot^{-1}$ is $(0, \pi)$.Since $\frac{2\pi}{3} \in (0, \pi)$,the principal value is $\frac{2\pi}{3}$.

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

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