Сosα = 1/√3, Cos2α - Cos6α=?
Сos2α - Cos6α = 2Sin4α Sin2α = 2*2Sin2αCos2α * 2SinαCos2α=
=2*2*2SinαCosα* (2Cos²α -1) *2SinαCosα = 16Sin²α Cos²α(2Cos²α-1) =
=16(1-Cos²α)Cos²α(2Cos²α -1) =
=16*(1 -1/3)*1/3*(2*1/3-1) = 16*2/3*1/3*(2/3-1)=16*2/3*1/3*(-1/3)=-32/27