cosec x = – 2 ⇒ sin x = $-\frac{1}{2}$ A value of x, satisfying sinx = $\frac{1}{2}$ is $\frac{\pi}{6}$ Principal Solution :We have, sinx = $-\frac{1}{2}$ Thus, sin $\left(\pi+\frac{\pi}{6}\right)$ = - sin $\frac{\pi}{6}$ = $-\frac{1}{2}$ and , sin $\left(2\pi-\frac{\pi}{6}\right)$ = - sin $\frac{\pi}{6}$ = $-\frac{1}{2}$ Thus, sin $\frac{7\pi}{6}$ = sin $\left(\frac{11\pi}{6}\right)$ = $-\frac{1}{2}$ Therefore principal solutions are $\frac{7\pi}{6},\frac{11\pi}{6}$ General Solution : sinx = $-\frac{1}{2}$ ⇒ sin x = sin $\left(\pi+\frac{\pi}{6}\right)$ ⇒ sin x = sin $\frac{7\pi}{6}$ ⇒ x = nπ + $(-1)^n \frac{7\pi}{6}$ , n ∊ Z Since if sin x = sin α , then x = nπ + $(-1)^n$ α , n ∊ Z