Question

3cos^2x+2sinxcosx+5sin^2x=3

Answer 1

$3\cos^2x+2\sin x\cos x+5\sin^2x=3(\sin^2x+\cos^2x)\\\\3\cos^2x+2\sin x\cos x+5\sin^2x=3\sin^2x+3\cos^2x\\\\2\sin^2x+2\sin x\cos x=0|:2\cos^2x\\\\tg^2x+tgx=0\Rightarrow\left \ [ {{tg x=0,} \atop {tg x=-1}} \right. \\\\\left \ [ {{z=arctg(0)+\pi k,} \atop {x=arctg(-1)+\pi k}} \right. \left \ [ {{x=\pi k,} \atop {x=-\frac{\pi}{4}+\pi k }} \right.$

ОТВЕТ: $x=\pi k, k\in\mathbb Z; x=-\frac{\pi}{4}+ \pi k, k\in\mathbb Z$.