$si{n}^{-1}[x\sqrt{1-x}-\sqrt{x}\sqrt{1-x^2}]=$

The correct option is C

$si{n}^{-1}x-si{n}^{-1}\sqrt{x}$

$si{n}^{-1}[x\sqrt{1-x}-\sqrt{x}\sqrt{1-x^2}]$
Substitute $x=sin\theta and\sqrt{x}=sin\varphi sothat\theta =si{n}^{-1}xand\varphi =si{n}^{-1}\sqrt{x}$
We get $si{n}^{-1}[sin\theta \sqrt{1-si{n}^2\varphi }-sin\varphi \sqrt{1-si{n}^2\theta }]$
$=si{n}^{-1}[sin\theta cos\varphi -sin\varphi cos\theta ]=si{n}^{-1}\left[sin\right(\theta -\varphi \left)\right]=\theta -\varphi =si{n}^{-1}x-si{n}^{-1}\sqrt{x}$