C3 - What exactly is "Harmonic Form"?

I've been asked by a class mate what 'harmonic form' is, because they missed the class. I've explained how to use it, but they're still confused, and the more I think about it, the more I wonder too. When I'm told to use harmonic form it's usually like so:

Express 3cosx + 7sinx in the form rcos(x-a)
or

Express 2cosx + 4sin x in the form rsin(x+a)

I know how to do this, but I don't understand the purpose of the form. When I search on Google for a meaning or definition of 'harmonic form' I found a few websites that showed me how to express in the form of rsin(x-a), etc. but they didn't actually tell me what it was.

Some websites called it 'harmonic identities' but when I looked at pages on 'harmonic form' and 'harmonic identities' on websites like Wikipedia, what I saw appeared to be completely unrelated to what I've been told is 'harmonic form', or far beyond my knowledge of it. When I open text books, they talk about expressing in the form rcos(x+a), etc. but they never call it harmonic form at all.

Can someone explain what 'harmonic form' actually means in this case, and what practical application it has? Or is this just a case of an exam board giving the identities
"bcosx + csinx = rcos(x-a)"
"bcosx + csinx = rcos(x+a)"
"bcosx + csinx = rsin(x-a)"
"bcosx + csinx = rsin(x+a)"
A catch all term that isn't officially recognised?
Thanks.

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