cos x = - $\frac{1}{2}$ ⇒ sec x = - 2 1 + $\tan^2 x$ = $\sec^2 x$ ⇒ $\tan^2 x$ = 4 - 1 ⇒ $\tan^2 x$ = 3 ⇒ tan x = ± $\sqrt{3}$ tan x = $\sqrt{3}$ [Since x lies in the third quadrant] ⇒ cot x = $\frac{1}{\sqrt{3}}$ ; sin x = tan x × cos x = $\sqrt{3} \times \left(-\frac{1}{2}\right)$ = $-\frac{\sqrt{3}}{2}$ ⇒ cosec = $-\frac{2}{\sqrt{3}}$