The value of $\sin (\cot ^{-1} x)$ is

The principal value of $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is equal to . . . . . . .

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...

$\cot^{-1}(-\sqrt{3}) = $

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

For the equation $\cos ^{-1} |x| + \cos ^{-1} |2x| = \pi$,the number of real solution$(s)$ is