Find all values of x such that sin 2x = sin x and 0 x 2π. (List the answers in increasing order.)

Question

x=
x=
x=
x=
x=

Answer 1

sin 2x - sinx = 0 , 0 < x < 2π

2sinx cosx - sinx = 0
sinx(2cosx - 1) = 0
sinx = 0 or cosx = 1/2

for sinx = 0
x = 0 , π , 1π

for cosx = 1/2
x = π/3 or x = 5π/3