Work Step by Step
Step 1. Use the Identify $sin(2x)=2sin(x)cos(x)$ and separate the original into two equations $sin(x)=0$ and $2cos(x)=1$ Step 2. For each equation, find the reference values in $[0,2\pi)$ and add $2k\pi $ to form general solutions. Step 3. Combine all the solutions for a complete set.