\(A=cos\frac{\pi}{5}+cos\frac{2\pi}{5}+cos\frac{3\pi}{5}+cos\frac{4\pi}{5}+cos\pi+cos\left(2\pi-\frac{4\pi}{5}\right)+...+cos\left(2\pi-\frac{\pi}{5}\right)\)
\(A=2\left(cos\frac{\pi}{5}+cos\frac{2\pi}{5}+cos\frac{3\pi}{5}+cos\frac{4\pi}{5}\right)-1\)
\(=2\left(cos\frac{\pi}{5}+cos\frac{2\pi}{5}+cos\left(\pi-\frac{2\pi}{5}\right)+cos\left(\pi-\frac{\pi}{5}\right)\right)-1\)
\(=2\left(cos\frac{\pi}{5}+cos\frac{2\pi}{5}-cos\frac{2\pi}{5}-cos\frac{\pi}{5}\right)-1\)
\(=-1\)
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