sin^8X+cos^8X+4sin^2Xcos^2x-2sin^4xcos^4X(化简)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 09:14:49
sin^8X+cos^8X+4sin^2Xcos^2x-2sin^4xcos^4X(化简)

sin^8X+cos^8X+4sin^2Xcos^2x-2sin^4xcos^4X(化简)
sin^8X+cos^8X+4sin^2Xcos^2x-2sin^4xcos^4X(化简)

sin^8X+cos^8X+4sin^2Xcos^2x-2sin^4xcos^4X(化简)
原式=sin^8X-2sin^4xcos^4X+cos^8X+4sin^2Xcos^2x
=(sin^4x-cos^4x)^2+4sin^2Xcos^2x
=[(sin^2x-cos^2x)(sin^2x+cos^2x)]^2+4sin^2Xcos^2x
=(sin^2x-cos^2x)^2+4sin^2Xcos^2x
=sin^4x-2sin^2Xcos^2x+cos^4x+4sin^2Xcos^2x
=sin^4x+2sin^2Xcos^2x+cos^4x
=(sin^2x+cos^2x)^2
=1

答案为1
化简过程:=sin^8X-sin^4xcos^4X+cos^8X-sin^4xcos^4X+4sin^2Xcos^2x
=sin^4X(sin^4X-cos^4X)+cos^4X(cos^4X-sin^4x)+4sin^2Xcos^2x
=sin^4X(sin^2X-cos^2X))+cos^4X...

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答案为1
化简过程:=sin^8X-sin^4xcos^4X+cos^8X-sin^4xcos^4X+4sin^2Xcos^2x
=sin^4X(sin^4X-cos^4X)+cos^4X(cos^4X-sin^4x)+4sin^2Xcos^2x
=sin^4X(sin^2X-cos^2X))+cos^4X(cos^2X-sin^2x)+4sin^2Xcos^2x
=(sin^4X-cos^4X)*(sin^2x-cos^2X)+4sin^2Xcos^2x
=(sin^2x-cos^2X)*(sin^2x-cos^2X)+4sin^2Xcos^2x
=(sin^2x=cos^2X)^2
=1

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