Answer
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.
Work Step by Step
$\frac{1}{2}sec~x-1=0$
$\frac{1}{2}sec~x=1$
$sec~x=2$
The period of $sec~x$ is $2\pi$. The solutions in the interval: $[0,2π)$ are:
$x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.
