Question

Find the exact solutions of sin (2x) - sin (x) = 0 in the interval [0, 2pi)

Answer 1

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

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

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

Sin(x)=0 => x [PiK]
Cos(x)=1/2 => x[Pi/3+(2PiK/3)

K=0 x=0
K=1 x=Pi
K=2 x=5Pi/3

So the answer is 0,Pi, 5Pi/3