Question

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

Answer 1

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