[tex]3sinx+cosx+sin^2x+cos^2x=0 \\ 3sinx+ \sqrt{1-sin^2x}+sin^2x+1-sin^2x=0 \\ 3sinx+ \sqrt{1-sin^2x}+1=0 \\ 9sin^2x+6sinx+1=1-sin^2x \\ 10sin^2x+6sinx=0 \\ 2sinx(5sinx+3)=0 \\ sinx=0;x=2k \pi \\
sinx=- \frac{3}{5} ;x=(- 1)^{n+1}*arcsin \frac{3}{5}+n \pi [/tex]
