Answer:
Step-by-step explanation:
[tex]2\sqrt{3}\cos ^2\left(A\right)=\sin \left(A\right)\\\mathrm{Subtract\:}\sin \left(A\right)\mathrm{\:from\:both\:sides}\\2\sqrt{3}\cos ^2\left(A\right)-\sin \left(A\right)=0\\-\sin \left(A\right)+\left(1-\sin ^2\left(A\right)\right)\cdot \:2\sqrt{3}=0\\\sin \left(A\right)=-\frac{2\sqrt{3}}{3},\:\sin \left(A\right)=\frac{\sqrt{3}}{2}\\\mathrm{Combine\:all\:the\:solutions}\\A=\frac{\pi }{3}+2\pi n,\:A=\frac{2\pi }{3}+2\pi n4[/tex]
