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

Let $\mathop {Lim}\limits_{x \to 0} \sec^{-1} \left( \frac{x}{\sin x} \right) = l$ and $\mathop {Lim}\limits_{x \to 0} \sec^{-1} \left( \frac{x}{\tan x} \right) = m$,then

The value of $2 \sin ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is

Find the value of $\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]$

If $\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\pi}{6}$, then $x=$

Evaluate the expression: $sec^2(\tan^{-1} 3) - \tan^2(sec^{-1} 3) = $