3sin^2x+3sinxcosx+2cos^2x=1  

[latex]3 sin^{2} x+3sinxcosx+2cos ^{2}x = sin^{2}x+ cos^{2} x [/latex] [latex]2sin^{2}x+3sinxcosx+ cos^{2}x=0 [/latex] Разделим на [latex] cos^{2}x [/latex] [latex]2 tg^{2}x+3tgx+1=0 [/latex] Сделаем замену [latex]y=tgx[/latex] [latex]2 y^{2} +3y+1=0[/latex] [latex]D=9-8=1[/latex] [latex] y_{1}=-2 [/latex] [latex] y_{2}=- \frac{1}{2} [/latex] [latex]tgx=-2[/latex] [latex]tgx=- \frac{1}{2} [/latex] [latex] x_{1} =-arctg2+ \pi k[/latex] [latex] x_{2} =-arctg \frac{1}{2} + \pi k[/latex]