InterviewSolution
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InterviewSolution
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If `tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/(x+4))=pi/4`, find the value of `x`. |
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Answer» The given equation may be written as `tan^(-1)(x-2)/(x-4)=pi/4-tan^(-1)(x+2)/(x-4)=tan^(-1)1-tan^(-1)((x+2)/(x+4))[therefore pi/4=tan^(-1)(1/(x+2))`. `therefore (x-2)/(x-4) =1/(x+3) rArr (x-2)(x+3)=(x-4)` `rArr x^(2)+x-6=x-4 rArr x^(2)=2 rArr x=+-sqrt(2)`. Hence, `x=+-sqrt(2)`. |
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