Find the value of
5Cdfrac%7B3%5Cpi%7D%7B9%7D%5Cright%29%2B%5Ccos%5Cleft%28%5Cdfrac%7B5%5Cpi%7D%7B9%7D%5Cright%29%2B%5Ccos%5Cleft%28%5Cdfrac%7B7%5Cpi%7D%7B9%7D%5Cright%29" id="TexFormula1" title=" \cos\left(\dfrac{\pi}{9}\right)+\cos\left(\dfrac{3\pi}{9}\right)+\cos\left(\dfrac{5\pi}{9}\right)+\cos\left(\dfrac{7\pi}{9}\right)" alt=" \cos\left(\dfrac{\pi}{9}\right)+\cos\left(\dfrac{3\pi}{9}\right)+\cos\left(\dfrac{5\pi}{9}\right)+\cos\left(\dfrac{7\pi}{9}\right)" align="absmiddle" class="latex-formula">
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1 answer:
Recall the identity,

(link to proof in the comments)
so that the required sum has a value of

Recall another identity,

which means

Then the sum's value reduces to 1/2.
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