求证sin^6A+cos^6A=1-3sin^2Acos^A

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求证sin^6A+cos^6A=1-3sin^2Acos^A求证sin^6A+cos^6A=1-3sin^2Acos^A求证sin^6A+cos^6A=1-3sin^2Acos^Asin^6A+cos

求证sin^6A+cos^6A=1-3sin^2Acos^A
求证sin^6A+cos^6A=1-3sin^2Acos^A

求证sin^6A+cos^6A=1-3sin^2Acos^A
sin^6A+cos^6A=(sin^2A+cos^2A)(sin^4A+cos^4A-sin^2Acos^2A)=sin^4A+cos^4A+2sin^2Acos^2A-32sin^2Acos^2A
=(sin^2A+cos^2A)^2-3sin^2Acos^A
=1-3sin^2Acos^A