Question 627391
sin 2x=sin x
sin(x+y)=sinx*cosy+siny*cosx
so, sin 2x or sin(x+x)=2sinxcosx
Substitute
2sinxcosx=sinx
2sinxcosx-sinx=0
sinx(2cosx-1)=0
By the zero product property
sinx=0   and   2cosx-1=0

sinx=0 when x=0,pie

2cosx-1=0
2cosx=1
cosx=1/2 when x=pie/3,5*pie/3