MCQ
Find the principal value of $cosec ^{-1}(-\sqrt{2})$
- A$-\frac{\pi}{6}$
- B$\frac{\pi}{3}$
- C$-\frac{\pi}{2}$
- ✓$-\frac{\pi}{4}$
We know that the range of the principal value branch of cosec $^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$ and $cosec \left(-\frac{\pi}{4}\right)=-\sqrt{2}$
Therefore, the principal value of $cosec ^{-1}(-\sqrt{2})$ is $-\frac{\pi}{4}$
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