`sin^(-1)(1-x)-2sin^(-1)x=pi/2` , then x is equal to (A) `0,1/2` (B) `1,1/2` (C) 0 (D) `1/2`

Explanation

It is given that, ` sin ^{-1}(1-x)-2 sin ^{-1} x=frac{pi}{2}`

let `x=sin y`

Thus, ` sin ^{-1}(1-sin y)-2 y=frac{pi}{2}`

`Rightarrow sin ^{-1}(1-sin y)=frac{pi}{2}+2 y`

`Rightarrow 1-sin y=sin (frac{pi}{2}+2 y)`

`Rightarrow 1-sin y=cos 2 y`

`Rightarrow 1-sin y=1-2 sin ^{2} y `

`Rightarrow 2 sin ^{2} {y}-sin {y}=0`

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