Solve: tan2x + tan x = 0

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April 23rd 2009, 09:00 AM
SarahGr

Solve: tan2x + tan x = 0

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April 23rd 2009, 09:09 AM
running-gag

Hi

You can use the trig identity $\tan(2x) = \frac{2\tan x}{1-tan^2x}$ and factor
April 23rd 2009, 11:58 AM
masters

Quote:

Originally Posted by SarahGr

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.
April 23rd 2009, 12:18 PM
running-gag

$\tan^2 x=3$ can also lead to $\tan x = -\sqrt{3}$

$x = 120^{\circ}$

$x = 300^{\circ}$
April 23rd 2009, 12:51 PM
e^(i*pi)

Quote:

Originally Posted by running-gag

$\tan^2 x=3$ can also lead to $\tan x = -\sqrt{3}$

$x = 120^{\circ}$

$x = 300^{\circ}$

$tan(x) = 0$ is also a solution

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

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

$x = 360^{\circ} \text { , } 2\pi \text { radians }$
April 23rd 2009, 12:54 PM
running-gag

Quote:

Originally Posted by e^(i*pi)

$tan(x) = 0$ is also a solution

Of course it is ! (Happy)
April 23rd 2009, 03:07 PM
SarahGr

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February 5th 2013, 06:41 AM
scottsophie

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°
February 5th 2013, 07:34 AM
Petrus

Re: Solve: tan2x + tan x = 0

Quote:

Originally Posted by masters

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:)?
February 5th 2013, 07:55 AM
scottsophie

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.
February 5th 2013, 08:58 AM
Petrus

Re: Solve: tan2x + tan x = 0

Thanks:) got it:) ii thought so.. but was not 100% it was correct:)