How do you solve sin 2x = sin x?

sin(2x) = sinx

=2sinxcosx – sinx = 0

=sinx(2cosx – 1) = 0

=sinx = 0 or cosx = 1/2

If sinx = 0, then x = kπ, k = 0, ±1, ±2,…

Note :

If cosx = 1/2, then x = π/3 + 2kπ, 5π/3 + 2kπ, k = 0, ±1, ±2, …

The solutions in the interval [0, 2π] are:

0, π, 2π, π/3, 5π/3

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