字典翻译 问答 小学 数学 1化简(1-cos四次方x-sin四次方x)除(1-cos六次方x-sin六次方x)2已知0
问题标题:
1化简(1-cos四次方x-sin四次方x)除(1-cos六次方x-sin六次方x)2已知0
问题描述:

1化简

(1-cos四次方x-sin四次方x)除(1-cos六次方x-sin六次方x)

2已知0

洪强宁回答:
  (1-cos四次方x-sin四次方x)除(1-cos六次方x-sin六次方x)   1-cos^4(x)-sin^4(x)   =sin^2(x)-sin^4(x)+cos^2(x)-cos^4(x)   =sin^2(x)[1-sin^2(x)]+cos^2(x)[1-cos^2(x)]   =sin^2(x)cos^2(x)+cos^2(x)sin^2(x)   =2sin^2(x)cos^2(x)   (1-cos六次方x-sin六次方x)   =[1-(cos^6(x)+sin^6(x)]   =[cos^2(x)-cos^6(x)+sin^2(x)-sin^6(x)]   ={cos^2(x)[1-cos^4(x)]+sin^2(x)[1-sin^4(x)]   ={cos^2(x)[sin^2(x)+cos^2(x)【1-cos^2(x)】+sin^2(x)[cos^2(x)+sin^2(x)【1-sin^2(x)】}   ={cos^2(x)[sin^2(x)+sin^2(x)cos^2(x)]+sin^2(x)[cos^2(x)+sin^2(x)cos^2(x)]}   =sin^2(x)cos^2(x)[1+cos^2(x)+1+sin^2(x)]   =3sin^2(x)cos^2(x)   (1-cos四次方x-sin四次方x)除(1-cos六次方x-sin六次方x)   =2sin^2(x)cos^2(x)/3sin^2(x)cos^2(x)   =2/3   已知0
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