InterviewSolution
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InterviewSolution
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If `sin^(-1)((sqrt(x))/2)+sin^(-1)(sqrt(1-x/4))+tan^(-1)y=(2pi)/3`, thenA. maximum value of `x^(2)+y^(2)` is `(49)/(3)`B. maximum value of `x^(2)+y^(2)` is 4C. minimum value of `x^(2)+y^(2)` is `(1)/(3)`D. minimum value of `x^(2)+y^(2)` is 3 |
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Answer» Correct Answer - A::C::D `sin^(-1)((sqrt(x))/(2))+sin^(-1)(sqrt(1-(x)/(4)))+tan^(-1)y=(2pi)/(3),x in [0,4]` `therefore sin^(-1)((sqrt(x))/(2))+cos^(-1)((sqrt(x))/(2))+tan^(-1)y=(2pi)/(3)` `therefore (pi)/(2)+tan^(-1)y=(2pi)/(3)` `therefore tan^(-1)y=(2pi)/(3)-(pi)/(2)=(pi)/(6)` `rArr =(1)/(sqrt(3))` `therefore` maximum value of `(x^(2)+y^(2))=16+(1)/(3)=(49)/(3)` and minimum value of `(x^(2)+y^(2))=(0)^(2)+(1)/(3)=(1)/(3)` |
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