利用立方和公式a^3+b^3=(a+b)(a^2-ab+b^2)进行化简.
sin^6 a+cos^6 a+3sin^2 a cos^2 a
=(sin^2 a)^3+(cos^2 a)^3+3sin^2 a cos^2 a
=(sin^2 a+cos^2 a)(sin^4 a-sin^2 a*cos^2 a+cos^4 a)+3sin^2 a cos^2 a
=1*(sin^4 a-sin^2 a*cos^2 a+cos^4 a)+3sin^2 a cos^2 a
=sin^4 a-sin^2 a*cos^2 a+cos^4 a+3sin^2 a cos^2 a
=sin^4 a +2sin^2 a*cos^2 a+cos^4 a
=(sin^2 a+cos^2 a)^2
=1^2
=1