Wednesday, December 14, 2016

trigonometry - Prove the following trigonometric identity without a calculator involved

I have to prove the following statement.




$$1+\cos{2\pi\over5}+\cos{4\pi\over5}+\cos{6\pi\over5}+\cos{8\pi\over5}=0$$




I have tried to use the sum of angles formula for cosine, but didn't get to a point where I'd be able to show that it is equal to $0$.

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