How do you prove that $$\cos(2\pi/n)+\cos(4\pi/n)+\cdots+\cos(2(n-1)\pi/n)=-1,$$ where $n \geq 2$?
Prove that $\cos(2\pi/n)+\cos(4\pi/n)+\cdots+\cos(2(k-1)\pi/n)=-1$
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trigonometry
induction
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0Please correct the identity you want to prove. Then my answer will apply. – 2012-09-13