solve tan x+tan(x+60)+tan(x+120)=3.pls answer this question in detail.

Just expand the function ..

Tan A +  (tan 60 + tan A )/(1-tan60.tanA) +  (tan (120) + tan A )/(1-tan120.tanA)

tan A +  [root(3) + tanA]/[1-root(3).tanA] + [ tan A - root(3) ] /[1 + root(3).tanA]

tanA +  [ root(3) + 3.tanA + tanA + root(3).tan^2A  + tanA - root(3) -root(3).tan^2A + 3.tanA ] / [ 1 - 3tan^2A ]

tanA + [ 8tanA] / [ 1-3tan^2A ]

[9tanA - 3.tan^3A ]/[1-3tan^2A]

= 3.tan3A   ( eqaul to RHS )

Hence proved

Regards

Arun(askIITians forum expert)