sinα-cosα=m 求sin^4α+cos^4α的值
问题描述：
sinα-cosα=m 求sin^4α+cos^4α的值
sinα-cosα=m 求sin^4α+cos^4α的值
答
sinα-cosα=m 1-2sinacosa=m^2 2sinacosa=1-m^2
sin^4α+cos^4α=(sin^2α+cos^2α)-2sin^2acos^2a=1-1/2(2sinacosa)^2
=1-1/2(1-2m^2+m^4)
=1/2+m^2-1/2m^4这一步不太会！2sin^2acos^2a=1-1/2(2sinacosa)^2