To solve the equation sin 2x - sin x = 0, we will use the trigonometric identity sin 2x = 2sin x cos x.
Substitute sin 2x = 2sin x cos x into the equation:
2sin x cos x - sin x = 0
Factor out sin x:
sin x(2cos x - 1) = 0
Now, we have two possibilities:
1) sin x = 0
2) 2cos x - 1 = 0
For sin x = 0:
x = kπ, where k is an integer.
For 2cos x - 1 = 0:
2cos x - 1 = 0
2cos x = 1
cos x = 1/2
Using the unit circle or the knowledge of cosine function values, we find x = π/3 + 2πk or x = 5π/3 + 2πk, where k is an integer.
Therefore, the solutions are:
x = kπ, x = π/3 + 2πk, x = 5π/3 + 2πk, where k is an integer.
\boxed{x = k\pi, \quad x = \frac{\pi}{3} + 2k\pi, \quad x = \frac{5\pi}{3} + 2k\pi, \quad \text{where } k \text{ is an integer}}