So you have tan x + tan (x + pi/3) +tan (x + 2pi/3)
=tan x + [tan x + 3]/(1 - 3 tan x ) + ( tan x - 3)/(1+ 3 tan x)
=tan x(1 - 3 tan 2 x ) + (tan x + 3)(1 + 3 tan x) + (tan x - 3)(1 - 3 tan x) 1 - 3 tan 2 x
= 9 tan x - 3 tan 3 x/ 1 - 3 tan 2 x = 3 (3tan x - tan 3 x)/1 - 3tan 2 x
= 3 tan 3x
So 3 tan 3 x = 3
Hence 3x = n pi + pi/4
So x = n pi/3 + pi/12
__________________________________________________________________________________________________________
From J.R.R. Tolkien's 'The Lord of the Rings':
All that is gold does not glitter
Not all who wander are lost
The old that is strong does not wither,
Deep roots are not reached by frost.
From ashes a fire shall be woken
From shadows a light shall spring
Renewed shall be blade that's broken
The crown less again shall be king.
Moderation Team
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+ tan (
/3) + tan (
3
