sinα-cosα=1/3,则cos4α=?

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sinα-cosα=1/3,则cos4α=?sinα-cosα=1/3,则cos4α=?sinα-cosα=1/3,则cos4α=?sinα-cosα=1/3(sinα-cosα)^2=1/9(sin

sinα-cosα=1/3,则cos4α=?
sinα-cosα=1/3,则cos4α=?

sinα-cosα=1/3,则cos4α=?
sinα-cosα=1/3
(sinα-cosα)^2=1/9
(sinα)^2+(cosα)^2-2sinαcosα=1/9
1-2sinαcosα=1/9
2sinαcosα=8/9
sin2α=8/9
cos2α=±√17/9
cos4α=(cos2α)^2-(sin2α)^2
=17/81-64/81
=-47/81