Q11 of 26 Page 1

Solve for x :


OR


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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