Question

cosП/7-cos2П/7+cos3П/7

Answer 1

cosπ/7-cos2π/7+cos3π/7⇒π/7=α⇒
cosα-cos2α+cos3α=(cos3α+cosα)-cos2a=
=2cos(3α+α)/2·cos(3α-α)/2-cos2α=2cos2α·cosα-cos2α=
=cos2α(cosα-1)=(2cos²α-1)(cosα-1)=(2cos²π/7 -1)(cosπ/7-1);