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(square root of 3) tan2 x= tan x

Solve for -180 <or= x <or= 180

 May 27, 2015

Best Answer 

 #2
avatar+118725 
+10

$$\\\sqrt3tan^2x=tanx\\
\sqrt3tan^2x-tanx=0\\
tanx(\sqrt3tanx-1)=0\\
tanx=0 \quad or \quad \sqrt3tanx-1=0\\
tanx=0 \quad or \quad tanx=\frac{1}{\sqrt3}\\
-180^0,\;\;0^0,\;\;180^0,\quad or \quad -150^0,\;\;30^0\\
$so all the solutions are$\\
x=-180^0,\;\;-150^0,\;\;0^0,\;\;30^0,\;\;180^0$$

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 May 27, 2015
 #1
avatar
0

i see you seven people online. I see you and I'm judging you for not answering this question. But seriously please help me.

 May 27, 2015
 #2
avatar+118725 
+10
Best Answer

$$\\\sqrt3tan^2x=tanx\\
\sqrt3tan^2x-tanx=0\\
tanx(\sqrt3tanx-1)=0\\
tanx=0 \quad or \quad \sqrt3tanx-1=0\\
tanx=0 \quad or \quad tanx=\frac{1}{\sqrt3}\\
-180^0,\;\;0^0,\;\;180^0,\quad or \quad -150^0,\;\;30^0\\
$so all the solutions are$\\
x=-180^0,\;\;-150^0,\;\;0^0,\;\;30^0,\;\;180^0$$

Melody May 27, 2015
 #3
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+5

Thank you very much for your solution. Feel silly for not realising all it takes is some simple equation re-arranging.

 May 27, 2015
 #4
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0

May be a silly question but can -30 be a solution? Why/why not?

 May 27, 2015
 #5
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+5

NEVERMIND i got it now. I was thinking of the wrong thing

 May 27, 2015

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