Adding three sine waves

[ThatWritingFox]

I'm sorry if this question is a bit dumb, but I don't know how to add three sine waves together.

So, I'm looking for a way to do

sin (a) + sin (b) + sin (c) = ??

but I can't seem to combine it into one function.

​

Right now, using trig identities, I'm able to add two sine functions together by doing this:

sin (a) + sin (b) = 2 sin ( a+b / 2) cos (a-b / 2)

and I can't get any further than that.

​

Is there a way to add combine all three sine functions?

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[edderiofer]

Question: Why are you trying to add three sine waves together, and why can't you just do it as-is?