Answer
$x=\frac{\pi}{4},\frac{3\pi}{4}$
Work Step by Step
Step 1. Using the Sum-to-Product Formula $sin(u)+sin(v)=2sin(\frac{u+v}{2})cos(\frac{u-v}{2})$, the equation becomes $2sin(x)cos(\frac{\pi}{4})=1$ or $sin(x)=\frac{\sqrt 2}{2}$.
Step 2. For $sin(x)=\frac{\sqrt 2}{2}$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{4},\frac{3\pi}{4}$
