Đáp án: 1
Giải thích các bước giải:
$sin^6\alpha+cos^6\alpha+3.sin^2\alpha.cos^2\alpha$
$=(sin^2\alpha+cos^2\alpha)(sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha)+3.sin^2\alpha.cos^2\alpha$
$=sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha+3.sin^2\alpha.cos^2\alpha$
(vì $sin^2\alpha+cos^2\alpha=1$)
$=sin^4\alpha+2sin^2\alpha.cos^2\alpha+cos^4\alpha$
$=(sin^2\alpha+cos^2\alpha)^2$
$=1$ (vì $sin^2\alpha+cos^2\alpha=1$)
