atan((x - 1)/(x - 2)) %2B atan((x %2B 1)/(x %2B 2))=pi/4 – InterviewSolution

InterviewSolution

1.	atan((x - 1)/(x - 2)) %2B atan((x %2B 1)/(x %2B 2))=pi/4
Answer» tan^-1(X)+tan^-1(y)=tan^-1(X+y/1-xy)hencetan^-1((x-1/x-2)+(X+1)/X+2)/1-(x-1/x-2)*(X+1)/(X+2))=tan^-1(1)cancelling tan^-1 on both sideshencex^2+2x-x-2+x^2-2x+x-2/(x^2-4)-(x^2-1)=1-(2x^2-4/3)=12x^2-4=-32x^2=1x^2=1/2X=+-1/√2value of X is +-1/√2

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