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`(d)/(dx)[sin^(-1)(xsqrt(1 - x)- sqrt(x)sqrt(1 - x^(2)))]` is equal toA. `(1)/(2sqrt(x(1-x)))-(1)/(sqrt(1-x^2))`B. `(1)/(sqrt(1-{xsqrt(1-x)-sqrt(x(1-x^2))}^2))`C. `(1)/(sqrt(1-x^2))-(1)/(2sqrt(x(1-x)))`D. `(1)/(sqrt(x(1-x)(1-x)^2))` |
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Answer» Correct Answer - C Let `y=sin^(-1)[xsqrt(1-x)-sqrt(1-x^2)]` Put `x=sin alpha and sqrt(x)= sin beta` `therefore y=sin^(-1)[sinalphasqrt(1-sin^(2)beta)-sinbetasqrt(1-sin^(2)alpha)]=sin^(-1)[sin(alpha-beta)]=alpha-beta` `=sin^(-1)x-sin^(-1)sqrt(x)` `rArr (dy)/(dx)=(1)/(sqrt(1-x^2))-(1)/(sqrt(1-x)).(1)/(2sqrt(x))=(1)/(sqrt(1-x^2))-(1)/(2sqrt(x(1-x)))` |
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