Solve for x in (0 ; 360) : 2 tan x - 1 = -tan (-x).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve 2 tan x - 1 = -tan (-x)

Now we know that tan -x = - tan x

2 tan x - 1 = -tan (-x)

=> 2 tan x - 1 = tan (x)

=> tan x - 1 = 0

=> tan x = 1

=> x = arc tan 1

=> x = 45 degrees and 225 degrees.

The required values of x = 45 degrees and x = 225 degrees

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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