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

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

Mar 20, 2015

#1
+95360
+5

$$\\\dfrac{sin[2(x-\frac{\pi}{3})]}{cos[2(x-\frac{\pi}{3})]} = \dfrac{\sqrt{3}}{3}\\\\\\ let\;\; x-\frac{\pi}{3}=\theta\\\\ \frac{sin[2\theta]}{cos[2\theta]} = \frac{\sqrt{3}}{3}\\\\ tan(2\theta)=\frac{1}{\sqrt3} 1st or 3rd quad\\\\ 2\theta=\frac{\pi}{6},\;\;\frac{7\pi}{6},\;\;\frac{13\pi}{6},\;\;\frac{21\pi}{6},\;\;....\\\\ \theta=\frac{\pi}{12},\;\;\frac{7\pi}{12},\;\;\frac{13\pi}{12},\;\;\frac{21\pi}{12},\;\;....\\\\ \theta=\frac{\pi+6n\pi}{12}\qquad where\;\; n\in Z \;\;(n is an integer)$$$. Mar 21, 2015 ### 1+0 Answers #1 +95360 +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