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If tan-1x1x+2 + tan-1x+1x+2 = π4, then find the value of x.

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L.H.S. =  tan-1x1x+2 + tan-1x+1x+2 

            =tan1[x1x+2+x+1x+21(x1x+2)(x+1x+2)]

             =tan1[2x243]

             =π4=tan1(1)

2x243=1

x=±12

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