If $\frac{\pi}{2} \le x \le \frac{3\pi}{2},$ then $\sin^{-1}(\sin x)$ is equal to

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

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

The value of $\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)$ is equal to

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

If the area of the region bounded by the parabola $y^2 = 4kx$ and the line $x = k$ (where $k > 0$) is $\frac{128}{3} \text{ sq. units}$, then the value of $\sin^{-1}(\frac{2}{k})$ is equal to...