已知sinα=-根号5\5,则sin^4α-cos^4α的值帮下忙.

已知sinα=-根号5\5,则sin^4α-cos^4α的值帮下忙.
已知sinα=-根号5\5,则sin^4α-cos^4α的值
帮下忙.

已知sinα=-根号5\5,则sin^4α-cos^4α的值帮下忙.
sin^4α-cos^4α
=(sin²α+cos²α)(sin²α-cos²α)
=-cos(2α)
=2sin²α-1
=2*(-√5/5)²-1
=2*（1/5）-1
=-3/5

sinα=-根号5\5
sin^2α=1/5
cos^2α=1-1/5=4/5
sin^4α-cos^4α=(sin^2α+cos^2α)(sin^2α-cos^2α)
=(sin^2α-cos^2α)
=1/5-4/5
=-3/5

sin^4α-cos^4α=（sin^2α+cos^2α）*（sin^2α-cos^2α）=sin^2α-cos^2α=1/5-4/5=-3/5