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Here is the problem I am stuck with: Is it true that for every positive integer $n > 1$, $$\sum\limits_{k=1}^n \cos \left(\frac {2 \pi k}{n} \right) =0= \sum \limits_{k=1}^n \sin \left(\frac {2 \pi k}{n} \right)$$ I'm imagining the unit circle and adding up the value of both trig functions separ...