Answer
$x=\frac{\pi}{6}+2n\pi$, $x=\frac{5\pi}{6}+2n\pi$, $x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.
Work Step by Step
$3~sec^2x-4=0$
$3~sec^2x=4$
$sec^2x=\frac{4}{3}$
$sec~x=±\frac{2}{\sqrt 3}=±\frac{2}{\sqrt 3}\frac{\sqrt 3}{\sqrt 3}=±\frac{2\sqrt 3}{3}$
The period of $sec~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$x=\frac{\pi}{6}$, $x=\frac{5\pi}{6}$, $x=\frac{7\pi}{6}$ and $x=\frac{11\pi}{6}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{\pi}{6}+2n\pi$, $x=\frac{5\pi}{6}+2n\pi$, $x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.
