Question

помогите!!!
3sin^2x+2sinxcosx=2

Answer 1

$3Sin^{2}x+2Sinx Cosx=2\\\\3Sin ^{2}x+2Sinx Cosx-2(Sin^{2}x+Cos^{2}x)=0\\\\Sin^{2}x+2Sinx Cosx-2Cos^{2}x=0|:Cos^{2}x,Cosx\neq0\\\\tg^{2}x+2tgx-2=0\\\\D=2^{2}-4*(-2)=4+8=12=(2\sqrt{3})^{2}\\\\1)tgx=\frac{-2-2\sqrt{3}}{2}=-1-\sqrt{3}=-(1+\sqrt{3})\\\\x=arctg(-(1+\sqrt{3}))+\pi n,n\in Z\\\\x_{1} =-arctg(1+\sqrt{3})+\pi n,n\in Z\\\\2)tgx=\frac{-2+2\sqrt{3}}{2}=\sqrt{3}-1\\\\x_{2}=arctg(\sqrt{3}-1)+\pi n,n\in Z$