化简sin^4X-cos^4X答案是-cos2X 求过程 谢谢

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化简sin^4X-cos^4X答案是-cos2X 求过程 谢谢
化简sin^4X-cos^4X
答案是-cos2X 求过程 谢谢

化简sin^4X-cos^4X答案是-cos2X 求过程 谢谢
sin^4X-cos^4X
=(sin^2 x + cos^2 x)(sin^2 x- cos^2 x)
=1*(-cos2x)
=-cos2x

原式=(sin²x+cos²x)(sin²x-cos²x)=-(cos²x-sin²x)=-cos(2x).

sin^4X-cos^4X
=(sin^2x+cos^2x)(sin^2x-cos^2x)
=sin^2x-cos^2x
=-cos2x

sin^4X-cos^4X =(sin^2X+cos^2X) (sin^2X-cos^2X) =1*(sin^2X-cos^2X) =1-2cos^2X=-cos2X

sin^4X-cos^4X = (sin^2x + cos^2x)*(sin^2x - cos^2x)=-(cos^2x-sin^2x )=-cos2x