InterviewSolution
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InterviewSolution
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If `x=sin^-1""(2t)/(1+t^2)` and `y=tan ^-1""(2t)/(1-t) " the n find " dy/dx.` |
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Answer» `x=sin^-1""(2t)/(1+t^2)=sin^-1""(2 tan theta)/(1+tan ^2)` `=sin ^-1(sin 2 theta)` `2 theta=2tan^-1 t` Let t= tan `theta ` `rArr dxdy=(2)/(1+t^2)` and `y =tan ^-1""(2t)/(1-t^2)=2 tan ^-1 t ` `rArr dy/dx =2/(1+t^2)` `therefore (dx)/(dy)=(dy//dt)/(dx//dt)=(2//(1+t^2))/(2//(1+t^2))=1.` |
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