Question

Find the principal solution of the equation $cosecx=-2$.

• 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, $cosecx=-2$
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.