There was an answered question in the morning but it is erased. Could you help me on that question.

"Let $\displaystyle \zeta$ be a primitive n-th root of unity over $\displaystyle \mathbb{Q}$, where n>2 and let $\displaystyle \alpha=\zeta+{\zeta}^{-1}$. Prove that $\displaystyle \alpha$ is algebraic over $\displaystyle \mathbb{Q}$ of degree $\displaystyle \frac{\varphi(n)}{2}.$ "