{sin ^{ - 1}}left[ {xsqrt {1 - x} - sqrt x sq | vedclass

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(B) Let $x = \sin 	heta$ and $\sqrt{x} = \sin \phi$.Then,$	heta = \sin^{-1}(x)$ and $\phi = \sin^{-1}(\sqrt{x})$.Substituting these into the express

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${\sin ^{ - 1}}x - {\sin ^{ - 1}}\sqrt x $

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(B) Let $x = \sin 	heta$ and $\sqrt{x} = \sin \phi$.Then,$	heta = \sin^{-1}(x)$ and $\phi = \sin^{-1}(\sqrt{x})$.Substituting these into the expression:${\sin ^{ - 1}}(x\sqrt {1 - x} - \sqrt x \,\sqrt {1 - {x^2}} )$$= {\sin ^{ - 1}}(\sin 	heta \sqrt {1 - {{\sin }^2}\phi } - \sin \phi \sqrt {1 - {{\sin }^2}	heta } )$$= {\sin ^{ - 1}}(\sin 	heta \cos \phi - \sin \phi \cos 	heta )$$= {\sin ^{ - 1}}(\sin (	heta - \phi ))$$= 	heta - \phi$$= {\sin ^{ - 1}}(x) - {\sin ^{ - 1}}(\sqrt x )$.

${\sin ^{ - 1}}\left[ {x\sqrt {1 - x} - \sqrt x \sqrt {1 - {x^2}} } \right] = $

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