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If `x=(1-t^(2))/(1+t^(2))` and `y=(2t)/(1+t^(2))`, then `(dy)/(dx)` is equal toA. `-(y)/(x)`B. `(y)/(x)`C. `-(x)/(y)`D. `(x)/(y)` |
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Answer» Correct Answer - C Given ` x = (1-t^(2))/(1+t^(2))` and ` y = (2t)/(1+t^(2))` Put `t = tan theta` in both the equations, we get `x = (1- tan^(2) theta)/(1+ tan^(2) theta) = cos 2 theta " ".....(i)` and ` y = (2 tan theta)/(1+tan^(2) theta) = sin 2 theta " ".....(ii)` On differenting both the Eqs. (i) and (ii) , we get `(dx)/(d theta) = - 2 sin 2 theta` and `(dy)/(d theta) = 2 cos 2 theta` `therefore " "(dy)/(dx) = ((dy)/(d theta))/((dx)/(d theta))` `= - (cos 2 theta)/(sin 2 theta) = - (x)/(y)` |
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