Question

Solve equation on the interval [0,2pi) of sinx=sin(2x)

Answer 1

first of all, of course it happen at x=0, so now assume
\[x\neq 0\] :
\[\sin(x)=\sin(2x)=\sin(x)\cos(x)\]
so we have
\[\cos(x)=1/2\] , where does that happen in your interval?

Answer 2

I meant
\[\sin(2x)=2\sin(x)\cos(x)\]