化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?
化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?
化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?
化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?
[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)]
=[1-cos^4 A-sin^4 A-2cos^2 A*sin^2 A+2cos^2 A*sin^2 A]/[1-(cos^2 A+sin^2 A)(cos^4 A-cos^2 A*sin^2 A+sin^4 A)]
=[1+2cos^2 A*sin^2 A-（cos^2 A+sin^2 A)]/[1-(cos^4 A-cos^2 A*sin^2 A+sin^4 A)]
=[1+2cos^2 A*sin^2 A-1]/[1-(cos^4 A+2cos^2 A*sin^2 A+sin^4 A)+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/[1-(cos^2 A+sin^2)^2+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/[1-1+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/(3cos^2 A*sin^2 A)
=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
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