InterviewSolution
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InterviewSolution
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If `tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/(x))=tan^(-1)(-7)+pi` then x =A. 2B. 3C. 4D. none of these |
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Answer» We know that `tan^(-1)x+tan^(-1)y=pi+tn^(-1)(x+y)/(1-xy)` If `xgt0ygt0and xy gt1` `therefore tan^(-1)(x+1)/(x-1)+tan^(-1)(x-1)/(x-1)xx(x-1)/(x)gt0` `and ((x+1)/(x-1)+(x-1)/(x))/(1-(x+1)/(x-1)xx(x-1)/(x)=-7` `rarr x in (-infty,-1)cup(1,infty) and (2x^(2)-x+1)/(1-x)=-7` `rarr x in(-infty,-1)cup(1,infty) and (x-2)^(2)=0` `rarr` x=2 |
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