Answer :

Given, tan - 1 (x - 1) + tan - 1 x + tan - 1 (x + 1) = tan - 1 (3x)


tan - 1 (x - 1) + tan - 1 (x + 1) = tan - 1 (3x) - tan - 1 x


We know that,



Also,






Similarly,




From, (1), (2) and (3) we get,




1 + 3x2 = 2 - x2


4x2 - 1 = 0


x = ±1/2


OR


Assume,


Tan - 12x = θ


2x = tan θ


Now, L.H.S becomes




3θ - 2θ


θ.


But θ = tan - 1x


Hence Proved.


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