Answer:
x = 240°, x = 300°
Step-by-step explanation:
Using the identity
sin x = [tex]\frac{1}{cosecx}[/tex] = [tex]\frac{1}{-\frac{2}{\sqrt{3} } }[/tex] = - [tex]\frac{\sqrt{3} }{2}[/tex] , then
x = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60° ← related acute angle
Since sin x < 0 then x is in 3rd / 4th quadrants
x = 180° + 60° = 240°
x = 360° - 60° = 300°
