Question

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

Answer 1

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

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