I'm curious if there is a way to combine sinusoids of multiple frequency into a single sinusoid? For example, I'm looking for a way to combine: Acos(2παt + φ) + Bcos(2πβt + χ) where A, α, φ, B, β, χ are scalar constants and α & β represent the frequency. I'd even be interested in a less complex solution to: cos(2παt) + cos(2πβt) if this is much simpler than the general form above. I found an incomplete explanation on here that does a transform and then recombines using complex numbers ending up with a cosine with an arctangent inside. https://www.physicsforums.com/showthread.php?t=372263 However, explanations of the process are probably better than just a discrete example alone.