Find the principal value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$.

Evaluate: $\cos \left(\sec ^{-1} 2\right)+\tan \left(\cot ^{-1} \sqrt{3}\right)+\sin\left(\operatorname{cosec}^{-1} \frac{2}{\sqrt{3}}\right) = $ ?

If the inverse trigonometric functions take principal values,then $\cos ^{-1}\left(\frac{3}{10} \cos \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)+\frac{2}{5} \sin \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to

$\cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)=\ldots$

If $f(x) = \frac{\sqrt{\operatorname{Cos}^{-1} x}}{\sqrt{2(1-x)}}$ for $x < 1$,then $\lim_{x \rightarrow 1^{-}} f(x) =$

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