sin^6a+cos^6a+3sin^2acos^2a的值为?

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sin^6a+cos^6a+3sin^2acos^2a的值为?

sin^6a+cos^6a+3sin^2acos^2a的值为?
sin^6a+cos^6a+3sin^2acos^2a的值为?

sin^6a+cos^6a+3sin^2acos^2a的值为?
sin^6a+cos^6a+3sin^2acos^2a
=(sin²a+cos²a)(sin^4a-sin^2acos^2a+cos^4a)+3sin^2acos^2a
=sin^4a-sin^2acos^2a+cos^4a+3sin^2acos^2a
=sin^4a+2sin^2acos^2a+cos^4a
=(sin²a+cos²a)²
=1²
=1

sin^6a+cos^6a+3sin^2acos^2a
=(sin^2a+cos^2a)(sin^4a-sin^2acos^2a+cos^4a)+3sin^2acos^2a
=sin^4a-sin^2acos^2a+cos^4a+3sin^2acos^2a
=sin^4a+2sin^2acos^2a+cos^4a
=(sin^2a+cos^2a)^2
=1^2
=1