Trigonometric identity $2\cos(\alpha)\cos(\beta) = \cos(\alpha + \beta) + \cos(\beta - \alpha)$ in a book. Is it correct? The identity should be $2\cos(\alpha)\cos(\beta) = \cos(\alpha + \beta) + \cos(\alpha - \beta)$, but in the book (see attached picture) states it as follows
$2\cos(\alpha)\cos(\beta) = \cos(\alpha + \beta) + \cos(\beta - \alpha)$. What am I missing?


note that $$\cos(A+B)+\cos(B-A)=\cos(A)\cos(B)-\sin(A)\sin(B)+\cos(B)\cos(A)+\sin(A)\sin(B)=2\cos(A)\cos(B)$$
