化简1/4sin2x shin4x-sin^8 X+cos^8 X化简1/4sin2x X shin4x-sin^8 X+cos^8 X

来源:学生作业帮助网 编辑:作业帮 时间:2024/08/05 22:15:34
化简1/4sin2x shin4x-sin^8 X+cos^8 X化简1/4sin2x X shin4x-sin^8 X+cos^8 X
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化简1/4sin2x shin4x-sin^8 X+cos^8 X化简1/4sin2x X shin4x-sin^8 X+cos^8 X
化简1/4sin2x shin4x-sin^8 X+cos^8 X
化简1/4sin2x X shin4x-sin^8 X+cos^8 X

化简1/4sin2x shin4x-sin^8 X+cos^8 X化简1/4sin2x X shin4x-sin^8 X+cos^8 X
cos^8 x-sin^8 x=(cos^4 x-sin^4 x)(cos^4 x+sin^4 x)
cos^4 x-sin^4 x=(cos^2 x-sin^2 x)(cos^2x+sin^2 x)=cos2x
cos^4 x+sin^4 x=(cos^2x+sin^2 x)^2-2cos^2x*sin^2 x=1-(sin2x)^2/2
所以cos^8 x-sin^8 x=cos2x-cos2x(sin2x)^2/2=cos2x-(sin4xsin2x)/4
所以1/4sin2x*sin4x-sin^8 x+cos^8 x=1/4sin2x*sin4x+cos2x-(sin2xsin4x)/4=cos2x