Cos0 + cos p/7 + cos 2p/7 +...+ cos 6p/7

Question

Cos0 + cos p/7 + cos 2p/7 +...+ cos 6p/7

Answer 1

Cos 6pi/7 = cos (pi - pi/7) = -cos pi/7
cos 5pi/7 = cos (pi - 2pi/7) = -cos 2pi/7
cos 4pi/7 = cos (pi - 3pi/7) = -cos 3pi/7

cos 0 + cos pi/7 + cos 2pi/7 + cos 3pi/7 - cos 3pi/7 - cos 2pi/7 - cos pi/7 =
= cos 0 = 1