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Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)...

Solve : `tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x`

Text Solution

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`tan^-1(x-1)+tan^-1x+tan^-1(x+1) = tan^-1(3x)`
`=>tan^-1(x-1)+tan^-1x = tan^-1(3x)-tan^-1(x+1)`
`=>tan^-1((x-1+x)/(1-x(x-1))) =tan^-1((3x-(x+1))/(1+3x(x+1)))`
`=>tan^-1((2x-1)/(1+x-x^2)) =tan^-1((2x-1)/(1+3x+3x^2))`
`=>(2x-1)/(1+x-x^2) =(2x-1)/(1+3x+3x^2)`
`=>(2x-1)/(1+x-x^2) - (2x-1)/(1+3x+3x^2) = 0`
`=>(2x-1)(1/(1+x-x^2) - 1/(1+3x+3x^2) )= 0`
`=>(2x-1)((1+3x+3x^2-1-x+x^2)/((1+x-x^2)(1+3x+3x^2) ))= 0`
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