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(sin2(x-(pi/3)))/(cos2(x-(pi/3) = sqrt(3)/3

Guest Mar 20, 2015

Best Answer 

 #1
avatar+93691 
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$$\\\dfrac{sin[2(x-\frac{\pi}{3})]}{cos[2(x-\frac{\pi}{3})]} = \dfrac{\sqrt{3}}{3}\\\\\\
let\;\; x-\frac{\pi}{3}=\theta\\\\
\frac{sin[2\theta]}{cos[2\theta]} = \frac{\sqrt{3}}{3}\\\\
tan(2\theta)=\frac{1}{\sqrt3}
$1st or 3rd quad$\\\\
2\theta=\frac{\pi}{6},\;\;\frac{7\pi}{6},\;\;\frac{13\pi}{6},\;\;\frac{21\pi}{6},\;\;....\\\\
\theta=\frac{\pi}{12},\;\;\frac{7\pi}{12},\;\;\frac{13\pi}{12},\;\;\frac{21\pi}{12},\;\;....\\\\
\theta=\frac{\pi+6n\pi}{12}\qquad where\;\; n\in Z \;\;$(n is an integer)$$$

Melody  Mar 21, 2015
 #1
avatar+93691 
+5
Best Answer

$$\\\dfrac{sin[2(x-\frac{\pi}{3})]}{cos[2(x-\frac{\pi}{3})]} = \dfrac{\sqrt{3}}{3}\\\\\\
let\;\; x-\frac{\pi}{3}=\theta\\\\
\frac{sin[2\theta]}{cos[2\theta]} = \frac{\sqrt{3}}{3}\\\\
tan(2\theta)=\frac{1}{\sqrt3}
$1st or 3rd quad$\\\\
2\theta=\frac{\pi}{6},\;\;\frac{7\pi}{6},\;\;\frac{13\pi}{6},\;\;\frac{21\pi}{6},\;\;....\\\\
\theta=\frac{\pi}{12},\;\;\frac{7\pi}{12},\;\;\frac{13\pi}{12},\;\;\frac{21\pi}{12},\;\;....\\\\
\theta=\frac{\pi+6n\pi}{12}\qquad where\;\; n\in Z \;\;$(n is an integer)$$$

Melody  Mar 21, 2015

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