Can someone explain me please why
$2 \vec U \vec V cos(\omega t + \phi _1)cos(\omega t + \phi _2) = U V cos(\alpha )cos(2\omega t + \phi _1+\phi _2)+(cos\phi _1 - \phi _2) $,
where $\alpha$ is the angle between the vectors $\vec U$ and $\vec V$.
I just don't see it, It's from my physics book and I don't understand this step. I tried to use $cos(a+b) = cos(a)cos(b) - sin(a)sin(b)$ but I think it's nonsense because of that $sin$ and I didn't find any trigonometry identity which would help me neither.