sinα+cosα=根号2则sin^4α-cos^4α=?
问题描述：
sinα+cosα=根号2则sin^4α-cos^4α=?
答
sinx+cosx=√2.两边平方
(sinx+cosx)^2=2
(sinx)^2+(cosx)^2+2sinxcosx=2
1+sin2x=2.
sin2x=1
cos2x=0
sin^4α-cos^4α
=(sin^2α-cos^2α)(sin^2α+cos^2α)
=sin^2α-cos^2α
=(sinα-cosα)(sinx+cosx)
=0*√2
=0