Question

cos a = 1/2 for all 0 ≤ α ≤ 2π

Answer 1

I think what they meant was
cos a = 1/2 for 0 ≤ a ≤ 2π
That is, all solutions in the interval [0,2π)
That would be a = π/3 or 5π/3

Answer 2

This statement is false.

At α = 0 and α = 2π, cos α = 1, but for other values of α, cos α can take on different values.

Answer 3

Yes, that statement is true. The solutions for cos a = 1/2 in the interval [0, 2π) are indeed a = π/3 or 5π/3.