Question

$\cos( \frac{2\pi}{7} ) + \cos( \frac{4\pi}{7 } ) + \cos( \frac{6\pi}{7} ) =$

Answer 1

$cos( \frac{2\pi}{7} ) + \cos( \frac{4\pi}{7 } ) + \cos( \frac{6\pi}{7} )\\ a =\frac{2\pi}{7}\\ cos(a)+cos(2a)+cos(3a)$

$cos{3a}+cos{a}=2cos\frac{3a+a}{2}*sin\frac{3a-a}{2}=\\ =2cos(2a)sin(a)$

$2cos(2a)sin(a)+cos(2a)=\\ cos2\alpha(\sin{\alpha}+1)$