# 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)

The following formula holds for $m,n \in \{0,1,2,\ldots\}$: $$2\cos(mt)\cos(nt)=\cos((m+n)t)+\cos((m-n)t),$$ where $\cos$ denotes cosine.