\(\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha.\cos^2\alpha\\=(\sin^6\alpha+\cos^6\alpha)+3\sin^2\alpha.\cos^2\alpha\\=(\sin^2\alpha+\cos^2\alpha)(\sin^4\alpha-\sin^2\alpha.\cos^2\alpha+\cos^4\alpha)+3\sin^2\alpha.\cos^2\alpha\\=\sin^4\alpha-\sin^2\alpha.\cos^2\alpha+\cos^4\alpha+3\sin^2\alpha.\cos^2\alpha\\=\sin^4\alpha+2\sin^2\alpha.\cos^2\alpha+\cos^4\alpha\\=(\sin^2\alpha+\cos^2\alpha)^2\\=1^2=1.\\\text{Giải thích:}\\\text{-Áp dụng hằng đẳng thức:}A^3+B^3=(A+B)(A^2-AB+B^2)\\\text{-Áp dụng công thức:}\sin^2\alpha+\cos^2\alpha=1.\)
