InterviewSolution
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InterviewSolution
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सरलतम रूप में लिखिए - `tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))), a gt 0 :(-a)/(sqrt3) le x le (a)/(sqrt3).` |
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Answer» माना `x=a tan theta` `rArr" "tan theta=(x)/(a)` `rArr" "theta=tan^(-1)((x)/(a))` चूँकि`" "-(a)/(sqrt3) lt x lt (a)/(sqrt3)` `rArr" "-(a)/(sqrt3) lt a tan theta lt (a)/(sqrt3)` `rArr" "-(1)/(sqrt3) lt tan theta lt (1)/(sqrt3)` 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^(3)(3tan theta-tan^(3)theta))/(a^(3)(1-3tan^(2)theta))]` `=tan^(-1)[(3tan theta-tan^(3)theta)/(1-3tan^(2)theta)]` `=tan^(-1)(tan3 theta)` `=3theta` `=3tan^(-1).(x)/(a)` जो कि अभीष्ट सरलतम रूप है। |
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