作业帮化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 22:09:06
![化简[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)] 等于多少?](/uploads/image/z/12516409-1-9.jpg?t=%E5%8C%96%E7%AE%80%5B1-cos%5E4%28A%29-sin%5E4%28A%29%5D%2F%5B1-cos%5E6%28A%29-sin%5E6%28A%29%5D+%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
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