+0

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

0
335
1

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

Guest Mar 20, 2015

#1
+92164
+5

$$\\\dfrac{sin[2(x-\frac{\pi}{3})]}{cos[2(x-\frac{\pi}{3})]} = \dfrac{\sqrt{3}}{3}\\\\\\ let\;\; x-\frac{\pi}{3}=\theta\\\\ \frac{sin[2\theta]}{cos[2\theta]} = \frac{\sqrt{3}}{3}\\\\ tan(2\theta)=\frac{1}{\sqrt3} 1st or 3rd quad\\\\ 2\theta=\frac{\pi}{6},\;\;\frac{7\pi}{6},\;\;\frac{13\pi}{6},\;\;\frac{21\pi}{6},\;\;....\\\\ \theta=\frac{\pi}{12},\;\;\frac{7\pi}{12},\;\;\frac{13\pi}{12},\;\;\frac{21\pi}{12},\;\;....\\\\ \theta=\frac{\pi+6n\pi}{12}\qquad where\;\; n\in Z \;\;(n is an integer)$$$Melody Mar 21, 2015 Sort: ### 1+0 Answers #1 +92164 +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

### 29 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details