已知sinx+cosx=根号2求下列各式的值 sin^4x-cos^4x

已知sinx+cosx=根号2求下列各式的值 sin^4x-cos^4x
已知sinx+cosx=根号2求下列各式的值 sin^4x-cos^4x

已知sinx+cosx=根号2求下列各式的值 sin^4x-cos^4x
sinx+cosx=√2
(sinx+cosx)^2=2
sin2x=1
cos2x=0
sin^4x-cos^4x
=(sin^2x+cos^2x)(sin^2x-cos^2x)
=(sin^2x-cos^2x)
=-cos2x
原式＝-cos2x＝0

(sinx+cosx)^2=2 2cosxsinx=1 sin2x=1 x=π/4
所以sin^4x-cos^4x=0
分解因式。。。
sin^4x-cos^4x=(cos^2x+sin^2x)(sin^2x-cos^2x)=(sinx+cosx)(sinx-cosx)=0
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