Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 \sin ^{-1} x + 3 \cos ^{-1} x = \frac{2 \pi}{5}$ is:

$3 \tan^{-1} a$ is equal to

$\tan \left(2 \tan ^{-1} \frac{1}{5} + \sec ^{-1} \frac{\sqrt{5}}{2} + 2 \tan ^{-1} \frac{1}{8}\right)$ is equal to.

Considering only the principal values of the inverse trigonometric functions,the value of $\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is:

If $\alpha$ and $\beta$ are the least and the greatest values of $f(x)=(\sin ^{-1} x)^2+(\cos ^{-1} x)^2$ for all $x \in [-1, 1]$ respectively,then $8(\alpha+\beta)=$

$2 \tan^{-1}(\cos x) = \tan^{-1}(\csc^2 x)$,then $x = $