Question

Упростите выражение: (sin 2+ 3cos2 )² + (cos2 - 3sin 2.)²

Answer 1

$(\sin\alpha+3\cos\alpha)^2+(\cos\alpha-3\sin\alpha)^2=\\\\=\sin^2\alpha+6\sin\alpha\cos\alpha+9\cos^2\alpha+\cos^2\alpha-6\sin\alpha\cos\alpha+9\sin^2\alpha=\\\\=10\sin^2\alpha+10\cos^2\alpha=10(\sin^2\alpha+\cos^2\alpha)=10$