已知cos2α=3/5,求sin^α-cos^4α的值

已知cos2α=3/5,求sin^α-cos^4α的值
已知cos2α=3/5,求sin^α-cos^4α的值

已知cos2α=3/5,求sin^α-cos^4α的值
cos2α=cos²α-sin²α=3/5
所以原式=(cos²α+sin²α)(cos²α-sin²α)
=1×3/5
=3/5

cos2a=1-sina^2=3/5,所以sina=2根号5/5
cos4a=1+cos2a^2=34/25
所以sina-cos4a=2根号5/5-34/25