Question

решить уравнение sinX+2cos2X=3/2

Answer 1

$sin x+2cos 2x=1.5~~|cdot 2\ 2sin x+4cos 2x=3\ 2sin x+4(1-2sin^2x)=3\ 2sin x+4-8sin^2x-3=0\ 8sin^2x-2sin x-1=0\ D=b^2-4ac=(-2)^2-4cdot 8cdot (-1)=36$

$sin x=-0.25~~~Rightarrow~~~ boxed{x=(-1)^{k+1}arcsin0.25+pi k,k in mathbb{Z}} \ \ sin x=0.5~~~Rightarrow~~~ boxed{x=(-1)^kcdotfrac{pi}{6}+pi k,k in mathbb{Z}}$