Question

已知sinx-cosx=1/2,求sin^4x+cos^4x的值

Answer 1

sin^4x+cos^4x=(sin^2x+cos^2x)-2sin^2xcos^2x=1-2sin^2xcos^2x

因为sinx-cosx=1/2

所以(sinx-cosx)^2=1/4

(sinx-cosx)^2==1-2sinxcosx

即 1-2sinxcosx=1/4

sinxcosx=3/8

sin^2xcos^2x=9/64

sin^4x+cos^4x=(sin^2x+cos^2x)-2sin^2xcos^2x=1-2sin^2xcos^2x=1-2*(9/64)

=23/32