已知sinα=2根号5/5,则sin6α-cos6α的值为_________________

已知sinα=2根号5/5,则sin6α-cos6α的值为_________________
已知sinα=2根号5/5,则sin6α-cos6α的值为_________________

已知sinα=2根号5/5,则sin6α-cos6α的值为_________________
sinα=2根号5/5,则cosα=根号5/5,
sin2α=2sinαcosα=2*2根号5/5*根号5/5=4/5
cos2α=2(cosα)^2-1=-3/5
sin3α=sin(2α+α)=sin2αcosα+cos2αsinα
=-2根号5/25
同理cos3α=cos(2α+α)=cos2αcosα-sin2αsinα
=-11根号5/25
sin6α=2sin3αco3sα=2*(-2根号5/25)*(-11根号5/25)=44/125
cos6α=2(cos3α)^2-1=117/125
故sin6α-cos6α=44/125-117/125=73/125
本题也可和差化积