# Chapter 7 - Trigonometric Identities and Equations - 7.6 Trigonometric Equations - 7.6 Exercises - Page 720: 21

$\frac{\pi}{4}$, $\frac{2\pi}{3}$, $\frac{5\pi}{4}$, $\frac{5\pi}{3}$

#### Work Step by Step

$(\cot x-1)(\sqrt{3}\cot x+1)=0$ $\cot x-1=0$ or $\sqrt{3}\cot x+1=0$ If $\cot x-1=0$: $\cot x=1$ $\tan x=\frac{1}{1}=1$ The only solutions in $[0, 2\pi)$ are $\frac{\pi}{4}$ and $\frac{5\pi}{4}$. If $\sqrt{3}\cot x+1=0$: $\sqrt{3}\cot x=-1$ $\cot x=-\frac{1}{\sqrt{3}}$ $\tan x=-\sqrt{3}$ The only solutions in $[0, 2\pi)$ are $\frac{2\pi}{3}$ and $\frac{5\pi}{3}$.

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