## Trigonometry 7th Edition

$\theta=\{30^o,150^o\}$
$sec(\theta)-2tan(\theta)=0$ $\frac{1}{cos(\theta)}-2\frac{sin(\theta)}{cos(\theta)}=0\;\;\;\;\;\;\;\;\;\;$ multiply each side by $cos(\theta)$. $1-2sin(\theta)=0$ $-2sin(\Theta )=-1\;\;\;\;\;\;\;\;\;\;$ subtract $1$ from each side. $sin(\Theta )=\frac{-1}{-2} \;\;\;\;\;\;\;\;\;\;\;$ divide each side by $-2$ $sin(\Theta )=\frac{1}{2}$ $\theta= sin^{-1}(\frac{1}{2})$ We know $sin(\theta)$ is positive in quadrant $I$ and quadrant $II$ $\theta=30^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=180^o-30^o=150^o$ $\theta=30^o\;\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\theta=150^o$ $\theta=\{30^o,150^o\}$