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## Main Question or Discussion Point

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.

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.