Use the double-angle formula of cosine: cos2x = 1 - 2sin²x. The given equation can be rewritten as follows: 1- 2sin²x = 1 - sinx ··· Eq.1
Let sinx = X. Plug X into Eq.1, we have: 1 - 2X² = 1 - X Factor the equation: X(2X - 1) = 0
We have X = 0, or X = 1/2.
When X = 0, sinx = 0. So, x = 0, π, or 2π (0≦x≦2π)
When X = 1/2, sinx = 1/2. So, x = π/6, or 5π/6 (0≦x≦2π)
Answer: x, which satisfies the given equation, is an element of the set { 0, π/6, 5π/6, π, 2π}.