y = arcsin(2x * sqrt(1 - x ^ 2)), - 1/(sqrt(2))

Question

\( y=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right),-\frac{1}{\sqrt{2}}<x<\frac{1}{\sqrt{2}} \)

Answer 1

Solving L.H.S.

\(=2\theta\)\(\) (As x = \(sin\theta\) )

​= 2 \(\times\)​ ​​​​​​sin^-1 x

= 2 sin^-1 x

= R.H.S