For integer `x`

$ \left(\cos 2\pi x\right) ^2=1$ and I can check this as follows

`Simplify[Cos[2 \[Pi] x]^2, Assumptions -> x \[Element] Integers] `

and get `1`

as an output. The same holds when `x`

is half-integer. How do I assume this in `Mathematica`

? More generally, is there a nice way to implement assumptions of the type say $ x\in 3\mathbb{Z}+2$ without redefining variables that I use?