Question

What integer solutions are there of `cos x = 1` ?

Answer 1

The only integer solution of `cos x = 1` is `x = 0`

Explanation:

I will assume that you mean `cos x = 1` where `x` is an integer.

Note that:

`cos 2npi = 1" "` for any integer `n`

and for no other values of the argument.

Further note that `pi` is irrational.

Hence `2npi` is only an integer when `n = 0`, since if `2npi = m` then `pi = m/(2n)`.