Question

Find all solutions in the interval [0, 2π).

2 sin2x = sin x

Answers:
x = π/3, 2π/3
x = π/2, 3π/2, π/3, 2π/3
x = 0, π, π/6, 5π/6
x= π/6, 5π/6

I want to say it is the final one. I know π/6 is an answer I just don't know how to find others.

Answer 1

2sin(2x)=sinx
=>2(2sinx cosx)=sinx
=>sinx(4cosx-1)=0
either sinx=0 or cosx=1/4, both satisfies the above equation.

Answer 2

Sorry I forgot the power sign on the sin. It is 2 sin^2x = sin x

Answer 3

ohk..
so, sinx(2sinx-1)=0
either sinx=0 or sinx=1/2.