sin^6a+cos^6a+3sin^2acos^2a的值为?
问题描述：
sin^6a+cos^6a+3sin^2acos^2a的值为?
答
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
答
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...