Cos П/5 + cos 2П/5 + cos 4П/5 + cos 6П/5

Question

Cos П/5 + cos 2П/5 + cos 4П/5 + cos 6П/5

Answer 1

Cos(π/5)+cos(2π/5)+cos(4π/5)+cos(6π/5)=
=cos(π/5+cos(2π/5)+cos(π-(π/5))+cos(π+(π/5)=
по формулам приведения
=cos(π/5+cos(2π/5)-cos(π/5)-сos(π/5)=
=cos(2π/5)-cos(π/5)=
формула cosα-cosβ=-2sin((α+β)/2)·sin((α-β)/2)
= - 2sin(3π/10)sin(π/10)