Question

[Lê Hồng Ngọc]

tính :

\(E=\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha\cdot\cos^2\alpha\)

\(F=3\sin^3\alpha+\cos^3\alpha-2\sin^6\alpha+\cos^6\alpha\)

\(G=\sqrt{\sin^4\alpha+4\cos^2\alpha}+\sqrt{\cos^4\alpha+4\sin^2\alpha}\)

Answer 1

[alibaba nguyễn]

E = sin^6 + cos^6 + 3sin^2.cos^2

= (sin^2 + cos^2)(sin^4 - sin^2.cos^2 + cos^4) + 3 sin^2.cos^2

= (sin^2 + cos^2)^2 - 3sin^2.cos^2 + 3sin^2.cos^2

= 1