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

Question

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

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Answer

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

$\cot \theta = \frac{{ - 1}}{{\sqrt 3 }}$

We know that $\theta \in (0,\pi )$

$\cot \theta = \cot \left( {\pi - \frac{\pi }{3}} \right)$

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

Therefore, principal value of ${\cot ^{ - 1}}\left( {\frac{{ - 1}}{{\sqrt 3 }}} \right) = \frac{{2\pi }}{3}$

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