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tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=...

`tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4.` find

Text Solution

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`tan^(-1)""(x-1)/(x-2)+tan^(-1)""(x+1)/(x+2)=(pi)/(4)`
`implies tan^(-1)""((x-1)/(x-2)+(x+1)/(x+2))/(1-(x-1)/(x-2)*(x+1)/(x+2))=tan^(-1)1`
`((x-1)(x+2)+(x+1)(x-2))/((x-2)(x+2)-(x-1)(x+1))=1`
`implies (x^(2)+x-2+x^(2)-x-2)/((x^(2)-4)-(x^(2)-1))=1`
`implies (2x^(2)-4)/(-3)=1implies 2x^(2)-4= -3`
`implies 2x^(2)=1 implies x^(2)=(1)/(2)impliesx=pm(1)/(sqrt(2))`
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