First, we'll re-write the right side term, based on the
fact that the tangent function is odd, so tg(-x)=-tgx.
The
equation will become:
2tanx-1=-(-tan
x)
We'll remove the
brackets:
2tan x-1 = tan
x
We'll subtract tan x both
sides:
2tan x-1 - tan x =
0
We'll combine lie terms:
tan
x - 1 = 0
We'll add 1:
tan x
=1
x=arctan1 + k*pi
But arctan
1= pi/4
x = pi/4
The tangent
is also positive in the 3rd quadrant, so x = pi + pi/4
x =
5pi/4
The possible values of the angle are
{pi/4 ; 5pi/4}.
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