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Math Help - Solve: tan2x + tan x = 0

  1. #1
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    Solve: tan2x + tan x = 0

    .
    Last edited by SarahGr; May 14th 2009 at 07:30 PM.
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  2. #2
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    Hi

    You can use the trig identity \tan(2x) = \frac{2\tan x}{1-tan^2x} and factor
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  3. #3
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    Quote Originally Posted by SarahGr View Post
    Solve: tan2x + tan x = 0

    I have no idea how to solve this one =[
    Hi SarahGr,

    Solve:

    \tan 2x + \tan x = 0

    Recall that \tan 2x=\frac{2 \tan x}{1-\tan^2 x}


    \frac{2 \tan x}{1-\tan^2 x}+ \tan x=0


    2 \tan x+\tan x(1-\tan^2 x)=0

    2 \tan x+ \tan x - \tan^3 x=0

    3 \tan x - \tan^3 x=0

    \tan x(3-\tan^2 x)=0

    3-\tan^2 x=0

    \tan^2 x=3

    \tan x = \sqrt{3}

    x = 60^{\circ} \ \ or \ \ \frac{\pi}{3} radians and 240^{\circ} \ \ or \ \ \frac{4\pi}{3} radians.
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  4. #4
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    \tan^2 x=3 can also lead to \tan x = -\sqrt{3}

    x = 120^{\circ}

    x = 300^{\circ}
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  5. #5
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    Quote Originally Posted by running-gag View Post
    \tan^2 x=3 can also lead to \tan x = -\sqrt{3}

    x = 120^{\circ}

    x = 300^{\circ}
    tan(x) = 0 is also a solution

    x = 0^o \text { , } 0 \text {  radians }

    x = 180^o \text { , } \pi \text {  radians }

    x = 360^{\circ} \text { , } 2\pi \text {  radians }
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  6. #6
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    Quote Originally Posted by e^(i*pi) View Post
    tan(x) = 0 is also a solution
    Of course it is !
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    Last edited by SarahGr; May 14th 2009 at 07:30 PM.
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  8. #8
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    Re: Solve: tan2x + tan x = 0

    overall, with tan(x)=0, tan(x)=√3, tan(x)=-√3

    between 0≤x≤360: x= 0, 60, 120, 180, 240, 300, 360
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    Re: Solve: tan2x + tan x = 0

    Quote Originally Posted by masters View Post
    Hi SarahGr,

    Solve:

    \tan 2x + \tan x = 0

    Recall that \tan 2x=\frac{2 \tan x}{1-\tan^2 x}


    \frac{2 \tan x}{1-\tan^2 x}+ \tan x=0


    2 \tan x+\tan x(1-\tan^2 x)=0

    2 \tan x+ \tan x - \tan^3 x=0

    3 \tan x - \tan^3 x=0

    \tan x(3-\tan^2 x)=0

    3-\tan^2 x=0

    \tan^2 x=3

    \tan x = \sqrt{3}

    x = 60^{\circ} \ \ or \ \ \frac{\pi}{3} radians and 240^{\circ} \ \ or \ \ \frac{4\pi}{3} radians.
    Hello masters!
    There is one step i did not understand


    \frac{2 \tan x}{1-\tan^2 x}+ \tan x=0 i did understand how u got that but ur next step i did not understand ( could not fined it on ur code when i try copy)

    any possible that some1 could explain?
    Last edited by Petrus; February 5th 2013 at 07:37 AM.
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  10. #10
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    Re: Solve: tan2x + tan x = 0

    you have (tan2x/1-tan2x) + tanx = 0
    You find a common denominator of 1-tan2x

    this gives you: tan2x + (tanx)(1-tan2x) = 0

    (this equation is all over '1-tan2x', but you can get rid of it by moving it to the other side of the '=' sign, and multiplying this by the 0).

    You then expand the brackets to get: tan2x + tanx - tan3x = 0

    You then simplify this to get: tan3x + tanx = 0

    Hope this helps.
    Thanks from Petrus
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  11. #11
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    Re: Solve: tan2x + tan x = 0

    Thanks got it ii thought so.. but was not 100% it was correct
    Last edited by Petrus; February 5th 2013 at 09:00 AM.
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