InterviewSolution
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InterviewSolution
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Prove that `tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a`. |
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Answer» Putting `x=atantheta`, we get `tan^(-1)(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=tan^(-1)((3a^(3)tantheta-a^(3)tan^(3)theta)/(a^(3)-3a^(3)tan^(2)theta))` `tan^(-1)(3tantheta-tan^(3)theta)/(1-3tan^(2)theta)=tan^(-1)(tan 3theta)` `=3theta=3tan^(-1)x/a`. Hence, `tan^(-1)(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)x/a`. |
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