# Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 50

$$x=\frac{\pi }{3}, \qquad x= \frac{2\pi }{3}, \\ x=\frac{4\pi }{3}, \qquad x= \frac{5\pi }{3}$$

#### Work Step by Step

We solve as follows: $$3\tan ^2 x -9=0 \quad \Rightarrow \quad \tan ^2 x = 3\quad \Rightarrow \quad \tan x = \pm \sqrt{3} \quad \Rightarrow \quad x=\frac{\pi }{3}+ n\pi, \quad \text{ or } \quad x=\frac{2\pi }{3} + n \pi \quad n \in \mathbb{Z}$$So, $x= \frac{\pi }{3}$, $x= \frac{2\pi }{3}$, $x= \frac{4\pi }{3}$, and $x=\frac{5\pi }{3}$ are the only solutions in the interval $[0, 2\pi )$.

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