how do i find all solutions to the equation in the interval [0, 2p]. cos x = sin 2x

Question

I am struggling with my precalc class and i cant seem to answer this one 

Answer 1

cos(x)=sin(2x)

cos(x)=2sin(x)cos(x) (double angle identity)

2sin(x)cos(x)-cos(x)=0

factor

cos(x)(2sin(x)-1)=0

cos(x)=0

cos(x)=0 when x=90º or x=270º

2sin(x)-1=0

2sin(x)=1

sin(x)=1/2

sin(x)=1/2 when x=30º or x=150º