InterviewSolution
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InterviewSolution
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`tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))),agt0 , = (a)/(sqrt(3)) lt x lt (a)/(sqrt(3))` को सरलतम रूप में लिखे | |
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Answer» `x = a tan theta` रखें | `because - (a)/(sqrt(3)) lt x lt (a)/(sqrt(3))` तथा `a gt 0` `therefore - (a)/(sqrt(3)) lt a tan theta lt (a)/(sqrt(3)) rArr - (1)/(sqrt(3)) lt tan theta lt (1)/(sqrt(3))` `rArr - (pi)/(3) lt theta lt (pi)/(3)" "...(1)` `because x = a tan theta therefore tan theta = (x)/(a) rArr theta = tan^(-1)""(x)/(a)" "...(2)` अब, `tan^(-1)[(3a^(2)x - x^(3))/(a^(3) - 3ax^(2))] = tan^(-1)[(3a^(2)a tan theta - a^(3)tan^(3)theta)/(a^(3)-3a a^(2)tan^(2)theta)]` ` = tan^(-1)[(a^(2)(3 tan theta-tan^(3)theta))/(a^(3)(1-3tan^(2)theta))] = tan^(-1)(tan 3theta)` `= (3theta) = 3 tan^(-1)""(x)/(a)" "`[(2) से] |
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