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Proving a trigonometric identity

Hey guys! I'm new at MH! (Hi)

I'm doing a long exercise where I need to prove this identity that I obtained myself (it's a sort of conjecture). I'm stuck though! I tried developing what's inside the square root in the first member, but it didn't get anything useful by doing that.

Could anybody help me or give me hints on how to approach it?

Thank you very much!

Re: Proving a trigonometric identity

The -1 in the first member is out of the cos

Re: Proving a trigonometric identity

Expand under the radical, apply a Pythagorean identity, then a double-angle identity for cosine.