Find the principal value of $cosec^{-1}(2)$.

The value of $\sin^{-1}\left(\cos \frac{53\pi}{5}\right)$ is

$2 \coth^{-1}(4) + \text{sech}^{-1}\left(\frac{3}{5}\right) = $

The solution of the inequality $(\cot^{-1}x)^2 - 5\cot^{-1}x + 6 > 0$ is:

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

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