作业帮化简:1/4sin2x乘sin4x-sinˆ8(x)+cosˆ8(x)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/05 03:07:33
化简:1/4sin2x乘sin4x-sinˆ8(x)+cosˆ8(x)
要过程啊.
要过程啊.
用到的公式
sin2x=2sinxcosx
cos2x=cos^2(x)-sin^2(x)
sin^2(x)+cos^2(x)=1
a^2-b^2=(a+b)(a-b)
1/4sin2x*sin4x-sin^8(x)+cos^8(x)
=(1/4)*2sin^2(2x)cos2x-[sin^4(x)+cos^4(x)][sin^4(x)-cos^4(x)]
=(1/2)sin^2(2x)(cos^2x-sin^2x)+[sin^4(x)+cos^4(x)][sin^2(x)+cos^2(x)][cos^2(x)-sin^2(x)]
=[(1/2)sin^2(2x)+sin^4(x)+cos^4(x)][cos^2(x)-sin^2(x)]
=[2sin^2(x)cos^2(x)+sin^4(x)+cos^4(x)][cos^2(x)-sin^2(x)]
=[sin^2(x)+cos^2(x)]^2[cos^2(x)-sin^2(x)]
sin2x=2sinxcosx
cos2x=cos^2(x)-sin^2(x)
sin^2(x)+cos^2(x)=1
a^2-b^2=(a+b)(a-b)
1/4sin2x*sin4x-sin^8(x)+cos^8(x)
=(1/4)*2sin^2(2x)cos2x-[sin^4(x)+cos^4(x)][sin^4(x)-cos^4(x)]
=(1/2)sin^2(2x)(cos^2x-sin^2x)+[sin^4(x)+cos^4(x)][sin^2(x)+cos^2(x)][cos^2(x)-sin^2(x)]
=[(1/2)sin^2(2x)+sin^4(x)+cos^4(x)][cos^2(x)-sin^2(x)]
=[2sin^2(x)cos^2(x)+sin^4(x)+cos^4(x)][cos^2(x)-sin^2(x)]
=[sin^2(x)+cos^2(x)]^2[cos^2(x)-sin^2(x)]
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