Question

已知sinx-cosx=根号三/3,求(sinx)^4+(cosx)^4

Answer 1

sinx-cosx=根号三/3
平方，得1-2sinxcosx=1/3
得sinxcosx=1/3
(sinx)^4+(cosx)^4=((sinx)^2+(cosx)^2)^2-2(sinx)^2*(cosx)^2=1-2(sinxcosx)^2=7/9

Answer 2

注意到sin^2x+cos^2x=1
所以sinx-cosx=根号三/3有1/3=(sinx-cosx)^2=1-2sinxcosx sinxcosx=1/3
sin^4x+cos^4x=(sin^2x+cos^2x)^2-2sin^2xcos^2x=1-2sin^2xcos^2x=1-2/9=7/9