# Trigonometric equation4tanx-1 = - 3tan(-x)

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You want to solve 4 tan x - 1 = - 3*tan(-x)

Now tan -x = - tan x

4 tan x - 1 = - 3*tan(-x)

=> 4*tan x - 1 = 3* tan x

=> tan x = 1

=> x = arc tan 1

=> x = pi/4 + n*pi and 5*pi/4

For the equation x = pi/4 + n*pi and x = 5*pi/4 + n*pi

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:

4tanx-1=-3(-tan x)

We'll remove the brackets:

4tan x-1 = 3tan x

We'll subtract 3tan x both sides:

4tan x-1 - 3tan 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