Short Quiz

If \(\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\cos ^{-1}\left(\frac{1-a^2}{1+a^2}\right)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\), where \(\left.a, x \in\right] 0,1\), then the value of \(x\) is

The value of \(\sin \left(2 \sin ^{-1}(\cdot 6)\right)\) is

If \(\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0\), then \(x\) is equal to

The value of \(\sin \left(2 \tan ^{-1}(.75)\right)\) is equal to