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12 tan^3 x = 4 tan x

 Oct 26, 2018
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\(12 tan^3 x = 4 tan x\\ let\;\; y=tanx\\ 12y^3 = 4y\\ 12y^3 -4y=0\\ 4y(3y^2 -1)=0\\ 4y(\sqrt{3}y -1)(\sqrt{3}y +1)=0\\ 4y=0,\;\;\;or\;\;\;\sqrt{3}y -1=0\;\;\;or\;\;\; \sqrt{3}y +1=0\\ y=0,\qquad y=\frac{1}{\sqrt{3}}\qquad or\qquad y=\frac{-1}{\sqrt{3}}\\ tanx=0,\qquad tanx=\frac{1}{\sqrt{3}}\qquad or\qquad tanx=\frac{-1}{\sqrt{3}}\\ x=n\pi,\qquad x=n\pi\pm \frac{\pi}{6}\qquad n\in Z\)

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 Oct 26, 2018

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