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TrigonometrySuperchallengeThe Unit Circle and Circular Functions

The Unit Circle and Circular Functions · Superchallenge problem

Let h(t)=cos⁡t1+2th(t) = \dfrac{\cos t}{1 + 2^t}. Evaluate exactly:

∑k=−66h ⁣(kπ6)=h(−π)+h ⁣(−5π6)+⋯+h ⁣(5π6)+h(π).\sum_{k=-6}^{6} h\!\left(\frac{k\pi}{6}\right) = h(-\pi) + h\!\left(-\frac{5\pi}{6}\right) + \cdots + h\!\left(\frac{5\pi}{6}\right) + h(\pi).