Answer:
[tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
If [tex]180^{\circ}<x<270^{\circ},[/tex] then angle [tex]x[/tex] is in the III quadrant.
Since [tex]\tan x=\sqrt{3},[/tex] then [tex]x=240^{\circ}\ [180^{\circ}+60^{\circ}][/tex] (we get angle in the III quadrant)
Consider [tex]\sin (x-210^{\circ}).[/tex]
If [tex]x=240^{\circ},[/tex] then
[tex]\sin (240^{\circ}-210^{\circ})\\ \\=\sin 30^{\circ}\\ \\=\dfrac{1}{2}[/tex]
