If $\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$,then the value of $\cos ^{-1} x+\sin ^{-1} y$ is

Find the number of solutions for the equation $\sin^{-1} x = 2 \tan^{-1} x$ (in principal values).

$\cot \left(\sum_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right) = $

If $2 \sinh^{-1}\left(\frac{a}{\sqrt{1-a^2}}\right)=\log \left(\frac{1+x}{1-x}\right)$, then $x$ is equal to

If $0 \leqslant \cos ^{-1} x \leqslant \pi$ and $\frac{-\pi}{2} \leqslant \sin ^{-1} x \leqslant \frac{\pi}{2}$,then at $x=\frac{1}{5}$ the value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ is

Suppose $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ for $a \neq 0$. If $S_a(x) = S_b(x)$ for $a \neq b$,then $x =$