If $\sin ^{-1} x=y,$ then

$\tan \left[ \frac{1}{2} \cos^{-1} \left( \frac{\sqrt{5}}{3} \right) \right] = $

$\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)+\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)=$ . . . . . . .

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 $\cos ^{-1}\left(\tan \left(\frac{7 \pi}{4}\right)\right)$ is

If $y = \sin^{-1} \left( \frac{2x}{1 + x^2} \right)$,where $0 < x < 1$ and $0 < y < \frac{\pi}{2}$,then $\frac{dy}{dx} = $