Question: Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align}

Answer:

\begin{align} Let \;\; cot^{-1}\left(\sqrt3\right)=y. \;\;Then,\;\; cot y = \sqrt3 = cot\left(\frac{\pi}{6}\right).\end{align}

We know that the range of the principal value branch of cot⁻¹ is

\begin{align} \left(0, \pi\right) and \;\;cot\left(\frac{\pi}{6}\right) = \sqrt3.\end{align}

Therefore, the principal value of

\begin{align} cot^{-1}\left(\sqrt 3\right) is \frac{\pi}{6}\end{align}

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Question: Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align}

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