化简sin^6a+cos^6+3sin^2acos^2a的结果是?
问题描述：
化简sin^6a+cos^6+3sin^2acos^2a的结果是?
答
原式=(sin²a+cos²a)(sin^4a-sin²acos²a+cos^4a)+3sin²acos²a
=1×(sin^4a-sin²acos²a+cos^4a)+3sin²acos²a
=sin^4a-sin²acos²a+cos^4a+3sin²acos²a
=sin^4a+2sin²acos²a+cos^4a
=(sin²a+cos²a)²
=1²
=1
答
原式=(sin²a+cos²a)(sin^4a-sin²acos²a+cos^4a)+3sin²acos²a
=1×(sin^4a-sin²acos²a+cos^4a)+3sin²acos²a
=sin^4a-sin²acos²a+cos^4a+3sin²acos²a
=sin^4a+2sin²acos²a+cos^4a
=(sin²a+cos²a)²
=1²
=1
答
sin^6α+cos^6α+3sin^2αcos^2α
=(sin^2a)^3+(cos^2a)^3+3sin^2αcos^2α
=(sin^2a+cos^2a)(sin^4a-sin^2acos^2a+cos^4a)+3sin^2αcos^2α
=sin^4a-sin^2acos^2a+cos^4a+3sin^2αcos^2α
=sin^4a+2sin^2acos^2a+cos^4a
=(sin^2a+cos^2a)^2
=1