have another stupid trigo [gen. sol.] problem
The first one doesn't include solutions of the form so it's no good.
The second and third are equivalent (I'm assuming you intend n as an integer so it can have positive and negative values, not just positive values). You can quickly see this if you substitute some consecutive values of n (n = 0, 1, 2, 3, -1 , -2 , -3 ....). Having said this, I favour the second one - just because that's how I like to write it myself. Note that the second and third contain all the solutions that the first gives .....