SOLUTION: Use an algebraic method to find the exact solution(s) for sin 2x = sin x, where 0 is less than or equal to x which is less than 2 pie (Please show work)

Question 627391: Use an algebraic method to find the exact solution(s) for sin 2x = sin x, where 0 is less than or equal to x which is less than 2 pie (Please show work)
Answer by hammy(9) (Show Source): You can put this solution on YOUR website!
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
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