Question

The value of ${\text{cosec}}^{-1}(-\sqrt{2})$ is

• A. $\frac{\pi }{6}$
• B. $-\frac{\pi }{4}$
• C. $-\frac{\pi }{6}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $-\frac{\pi }{4}$

${\text{cosec}}^{-1}(-\sqrt{2})=-{\text{cosec}}^{-1}\left(\sqrt{2}\right)(\because {\text{cosec}}^{-1}(-x)=-{\text{cosec}}^{-1}x,|x|\ge 1)\Rightarrow {\text{cosec}}^{-1}(-\sqrt{2})=-\frac{\pi }{4}$