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

$e^{\log (\cosh^{-1} 2)}$ is equal to :

If $x$ is a real number,then the number of solutions of $\operatorname{Tan}^{-1}(\sqrt{x(x+1)})+\operatorname{Sin}^{-1}(\sqrt{x^2+x+1})=\frac{\pi}{2}$ is:

If $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,then $\cos^{-1}(\sin \theta)$ is equal to

Find the principal value of $cosec^{-1}(2)$.

If ${\cos ^{ - 1}}\left( {\frac{1}{x}} \right) = \theta $,then $\tan \theta =$