Question

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

Answer 1

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

$\Rightarrow \cot y=\sqrt{3}=\cot \left(\frac{\pi }{6}\right)$.

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

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