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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