InterviewSolution
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InterviewSolution
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If `tan^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=a`, show that `(dy)/(dx)=(x(1-tana))/(y(1+tana)).` |
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Answer» `tan^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=arArr((x^(2)-y^(2))/(x^(2)+y^(2)))=tana` `therefore (x^(2)-y^(2))=(x^(2)+y^(2)) tan a." …(i)"` On differentiating both sides of (i) w.r.t. x, we get `2x-2y.(dy)/(dx)=2x tan a +2y.(dy)/(dx).tana` `rArr y(1+tana)(dy)/(dx)=x(1-tana)` `rArr (dy)/(dx)=(x(1-tana))/(y(1+tana)).` |
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