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
=(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