Question

Cosπ/5+Cos2π/5+Cos4π/5+Cos6π/5

Answer 1

Ответ:

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)