问题标题:
求证!cos^8x-sin^8x+1/4sin2xsin4x=cos2x求数学大神帮忙详细过程谢谢
更新时间:2024-05-13 09:09:21
问题描述:

求证!cos^8x-sin^8x+1/4sin2xsin4x=cos2x

求数学大神帮忙详细过程谢谢

郎一民回答:
  cos^8x-sin^8x+1/4sin2xsin4x-cos2x   =(cos^4x+sin^4x)(cos^4x-sin^4x)+1/2sin²2xcos2x-cos2x   =(cos^4x+sin^4x)(cos²x-sin²x)+2sin²xcos²x(cos²x-sin²x)-cos2x   =cos^6x-sin^6x+sin²xcos^4x-sin^4xcos²x-cos2x   =cos^4x-sin^4x-cos2x   =cos²x-sin²x-cos2x   =cos2x-cos2x   =0   所以cos^8x-sin^8x+1/4sin2xsin4x-cos2x=0   cos^8x-sin^8x+1/4sin2xsin4x=cos2x
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