If ${\sin ^{ - 1}}\frac{1}{2} = {\tan ^{ - 1}}x,$ then $x =$

$\sin (\tan^{-1} x)$,where $|x| < 1$,is equal to:

The value of $\sin^{-1}\left(\sin \frac{5\pi}{3}\right)$ is equal to . . . . . . .

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

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

The principal value of $\cos^{-1}[\cos(-680^{\circ})]$ is equal to: . . . . . . .