How do you solve 3sec^2x - 4=0?

Jul 25, 2018

$x = \frac{\pi}{6} , \frac{5 \pi}{6} , \frac{7 \pi}{6} , \frac{11 \pi}{6}$ in the domain $0 \le x \le 2 \pi$

Explanation:

$3 {\sec}^{2} x = - 4 = 0$
${\sec}^{2} x = \frac{4}{3}$
$\frac{1}{\cos} ^ 2 x = \frac{4}{3}$
${\cos}^{2} x = \frac{3}{4}$
$\cos x = \pm \frac{\sqrt{3}}{2}$
$x = \frac{\pi}{6} , \pi - \frac{\pi}{6} , \pi + \frac{\pi}{6} , 2 \pi - \frac{\pi}{6}$
$x = \frac{\pi}{6} , \frac{5 \pi}{6} , \frac{7 \pi}{6} , \frac{11 \pi}{6}$ in the domain $0 \le x \le 2 \pi$