Find the principal values of the following: $cot^{-1} (\sqrt 3)$

$\begin{array}{1 1} \frac{\pi}{3} \\ \frac{-\pi}{3} \\ \frac{\pi}{6} \\ \frac{-\pi}{6} \end{array}$

Ans : $$cot^{-1}cot\frac{\pi}{6}=\frac{\pi}{6}$$
edited Mar 4, 2016 by meena.p

Toolbox:
• The range of the principal value of $\; cot^{-1}x$ is $\left [ 0,\pi \right ]$
Let $cot^{-1}\sqrt 3 = x \Rightarrow cot (x) = \sqrt 3$
We know that the range of the principal value of $\; cot^{-1}x$ is $\left [ 0,\pi \right ]$
Therefore, $cot(x) = \sqrt 3 = cot \frac{\pi}{6}$
$\Rightarrow x=\frac{\pi}{6}$, where $x \;\epsilon\;$ $\left [ 0,\pi \right ]$
Therefore, the principal value of $cot^{-1}(\sqrt 3) is \frac{\pi}{6}$