This question seems really hard, I'm trying to prove that the set of the adherent values of the sequence $x_n=\cos (n)$ is the closed interval $[-1,1]$, i.e., every point of this interval is a limit of a subsequence of $x_n$, and also the limit of any subsequence of $(x_n)$ is in $[-1,1]$

It's obvious that every adherent values is in $[-1,1]$, I'm having troubles to prove the converse, i.e., a point in $[-1,1]$ is an adherent value of $(x_n)$.

I need help

Thanks a lot