InterviewSolution
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InterviewSolution
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If `x=a^sqrt[sin^-1t]` and `y=a^sqrt[cos^-1t]`, then show that `[dy]/[dx]=-y/x` |
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Answer» We have `x^(2)=a^(sin^(-1)t) and y^(2)=a^(cos^(-1)t)` `rArr2x(dx)/(dt)=a^(sin^(-1)t).(1)/(sqrt(1-t^(2)))and2y(dy)/(dt)=a^(cos^(-1)t).((-1))/(sqrt(1-t^(2)))` `rArr(2y)/(2x).((dy//dt))/((dx//dt))=(-a^(cos^(-1)t))/(sqrt(1=t^(2)))xx(sqrt(1-t^(2)))/(a^(sin^(-1)t))` `rArr(y)/(x).(dy)/(dx)=(a^(cos^(-1)t))/(a^(sin^(-1)t))=-(y^(2))/(x^(2))` `rArr(dy)/(dx)=(-y)/(x)" "["on dividing both sides by "(y)/(x)].` Hence,`(dy)/(dx)=(-y)/(x).` |
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