Find the principal values of: ^ -1 (-3) - Vidyadip

Question

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

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Answer

(a) : Let $\cot ^{-1}(-\sqrt{3})=\theta \Rightarrow \cot \theta=-\sqrt{3}=-\cot \frac{\pi}{6}$
$=\cot \left(\pi-\frac{\pi}{6}\right)=\cot \frac{5 \pi}{6} \Rightarrow \theta=\frac{5 \pi}{6} \in(0, \pi)$
$\therefore$ Principal value of $\cot ^{-1}(-\sqrt{3})$ is $\frac{5 \pi}{6}$.

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