If `y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2])`and `0

1.	If `y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2])`and `0
Answer» `y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]," where "0lt x lt 1` `=sin^(-1)[xsqrt(1-(sqrt(x))^(2))-sqrt(x)sqrt(1-x^(2))]` `=sin^(-1)x-sin^(-1)sqrt(x)` `[because sin^(-1) x-sin^(-1)y=sin^(-1)(xsqrt(1-y^(2))-ysqrt(1-x^(2)))]` Differentiating w.r.t.x, we get `(dy)/(dx)=(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-(sqrt(x))^(2)))(d)/(dx)(sqrt(x))` `=(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-x))xx(1)/(2sqrt(x))`

Discussion

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