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TrigonometrySuperchallengeThe Unit Circle and Circular Functions

The Unit Circle and Circular Functions · Superchallenge problem

Evaluate exactly, using symmetry rather than adding term by term:

cos⁡2π5+cos⁡4π5+cos⁡6π5+cos⁡8π5+cos⁡10π5.\cos\dfrac{2\pi}{5}+\cos\dfrac{4\pi}{5}+\cos\dfrac{6\pi}{5}+\cos\dfrac{8\pi}{5}+\cos\dfrac{10\pi}{5}.
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