Hello,
[tex]2*\sqrt{3}*\dfrac{cos(x)}{sin(x)}+4*cos(x)- \dfrac{3}{sin(x)} +2*\sqrt{3}\\
=2*cos(x)*(\dfrac{\sqrt{3}}{sin(x)}+2)-\sqrt{3}(\dfrac{\sqrt{3}}{sin(x)}+2)\\
=(\dfrac{\sqrt{3}}{sin(x)}+2)*(2*cos(x)-\sqrt{3})\\\\
cos(x)=\dfrac{\sqrt{3}}{2} -\ \textgreater \ x=\dfrac{\pi}{6}\ or\ x=\dfrac{11*\pi}{6}\\
or\\
\dfrac{\sqrt{3}}{sin(x)}+2=0-\ \textgreater \ sin(x)=-\dfrac{\sqrt{3}}{2}-\ \textgreater \ x=\dfrac{5*\pi}{3}\ or\ x=\dfrac{4*\pi}{3}\\\\
[/tex]
