Question

Find the principal value of cot-1$\sqrt3$

Answer 1

Let cot-1$(\sqrt3)=y.$
Then cot y= (√3)= cot $\bigg(\frac{\pi}{6}\bigg)$
We know that the range of the principal value branch of cot-1 is
$\bigg(0,\pi\bigg) and \, cot\bigg(\frac{\pi}{6}\bigg)=\sqrt3.$
Therefore, the principal value of cot-1$(\sqrt3)$ is $\frac{\pi}{6}.$