Question

sinteză la matematica​

Answer 1

$E=(3\sin \alpha+2\cos \alpha)^2+(2\sin \alpha - 3\cos \alpha)^2\\ \\ =(9\sin^2 \alpha+12\sin \alpha\cos \alpha+4\cos^2\alpha)+(4\sin^2 \alpha-12\sin \alpha\cos \alpha+9\cos^2\alpha)\\ \\ =13\sin^2 \alpha+13\cos^2 \alpha\\ \\ = 13\cdot (\sin^2 \alpha+\cos^2 \alpha)\\ \\ = 13\cdot 1\\ \\ =\boxed{13}$