Question

Find the principal value $cosec^{-1} \left(\frac{-2}{\sqrt{3}}\right)$

• A. $-\frac{\pi}{3}$
• B. $\frac{\pi}{3}$
• C. $\frac{\pi}{2}$
• D. $-\frac{\pi}{2}$

Answer 1

Answer: (A)

Let $cosec^{-1} \left(\frac{-2}{\sqrt{3}}\right) = \theta$
$\Rightarrow cosec\,\theta = \frac{-2}{\sqrt{3}}$
$= -cosec \frac{\pi}{3}$
$= cosec \left(\frac{-\pi }{3}\right)$
$\Rightarrow \theta = \frac{-\pi }{3} \in \left[\frac{-\pi }{2}, \frac{\pi }{2}\right] - \left\{0\right\}$
$\therefore$ Principal value of $cosec^{-1} \left(\frac{-2}{\sqrt{3}}\right) is \left(\frac{-\pi }{3}\right)$