Question

Find the principal solution of the equation $cosec \,x = -2$.

• A. $\frac{\pi}{6}$, $\frac{7\pi}{6}$
• B. $\frac{\pi}{6}$, $\frac{11\pi}{6}$
• C. $\frac{7\pi}{6}$, $\frac{11\pi}{6}$
• D. None of these

Answer 1

Answer: (C)

We have, $cosec\, x = - 2$
We know that, $cosec\left(\pi+\frac{\pi}{6}\right)=-cosec \frac{\pi}{6}=-2$
Also, $cosec\left(2\pi-\frac{\pi}{6}\right)=-cosec\, \frac{\pi}{6}=-2$
Thus, $\pi+\frac{\pi}{6}$ and $2\pi-\frac{\pi}{6}$
i.e., $\frac{7\pi}{6}$ and $\frac{11\pi}{6}$ are the required principal solutions.