Determine the number of roots of the equation sin2x = sinx belonging to the interval (-3; 3)

According to the double angle formula sin (2x) = 2 * sin (x) * cos (x), therefore:

sin (2x) = sin (x) is equivalent to the equation 2 * sin (x) * cos (x) – sin (x) = 0, which is equivalent to:

(2 * cos (x) – 1) * sin (x) = 0

Equality is true in two cases.

Or sin (x) = 0, then x = 0 + pi * n, where n is an integer.

Either 2 * cos (x) – 1 = 0, then cos (x) = 1/2, which means x = ± pi / 3 + 2 * pi * n, where n is an integer.

Of the roots indicated for both cases, the interval (-3; 3) belongs to: -pi / 3; 0; pi / 3 – only 3 roots.

Answer: 3 roots.