化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?急用!

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化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?急用!
化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?急用!

化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?急用!
分子=1-(cos^4A+sin^4A)
=1-[(sin²A+cos²A)²-2sin²Acos²A]
=2sin²Acos²A
分母立方和=1-(sin²A+cos²A)(cos^4A-sin²Acos²A+sin^4A)
=1-(cos^4A+sin^4A)+sin²Acos²A
=3sin²Acos²A
原式=2/3

1-cos^4(A)-sin^4(A)
=1-[cos^2(A)+sin^2(A)]^2+2sin^2(A)cos^2(A)
=2sin^2(A)cos^2(A)
1-cos^6(A)-sin^6(A)
=1-[cos^2(A)+sin^2(A)]{[cos^2(A)+sin^2(A)]^2-3sin^2(A)cos^2(A)}
=3sin^2(A)cos^2(A)
原式=2/3

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