Find all solutions to cos2x=sinx in the interval (0, 2π)

Question

Pre calc problem

Answer 1

cos(2x)=1-2sin²(x)=sin(x), 2sin²(x)+sin(x)-1=0=(2sin(x)-1)(sin(x)+1), so sin(x)=1/2, x=π/6, 5π/6; or sin(x)=-1, x=3π/2.