Question

Rút gọn M=sin⁴\(\alpha\).(3-2sin²\(\alpha\)) + cos⁴\(\alpha.\left(3-2cos^2\alpha\right)\)

Answer 1

\(\sin^4a.\left(3-2\sin^2a\right)+\cos^4a\left(3-2\cos^2a\right)\)

\(=3\sin^4a-2\sin^6a+3\cos^4a-2\cos^6a\)

\(=3\left(\sin^4a+\cos^4a\right)-2\left(\sin^6a+\cos^6a\right)\)

\(=3\left(\left(\sin^2a\right)^2+\left(\cos^2a\right)^2\right)-2\left(\left(\sin^2a\right)^3+\left(\cos^2a\right)^3\right)\)

\(=3.1-2\left(sin^2a+\cos^2a\right)\left(\sin^4-sin^2.\cos^2+\cos^4\right)\)

\(=3-2.1\left(\left(\sin^2a\right)^2+\left(\cos^2a\right)^2\right).\left(-\sin^2.\cos^2\right)\)

\(=3-2\left(-\sin^2.\cos^2\right)\)