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Mark the tick against the correct answer in the following: The principal value of \operatorname{cosec}^{-1}(-\sqrt{2}) is
A. \frac{-\pi}{4}
B. \frac{3 \pi}{4}
C. \frac{5 \pi}{4}
D. none of these
CBSE | Class 12 | Inverse Trigonometric Functions | Maths | RS Aggarwal
Mark the tick against the correct answer in the following: The principal value of \operatorname{cosec}^{-1}(-\sqrt{2}) is
A. \frac{-\pi}{4}
B. \frac{3 \pi}{4}
C. \frac{5 \pi}{4}
D. none of these

Solution:

Option(A) is correct.
To Find: The Principle value of \operatorname{cosec}^{-1}(-\sqrt{2})
Let the principle value be given by \mathrm{x}
Now, let x=\operatorname{cosec}^{-1}(-\sqrt{2})
\begin{array}{l} \Rightarrow \operatorname{cosec} x=-\sqrt{2} \\ \Rightarrow \operatorname{cosec} x=-\operatorname{cosec}\left(\frac{\pi}{4}\right)\left(\because \operatorname{cosec}\left(\frac{\pi}{4}\right)=\sqrt{2}\right) \\ \Rightarrow \operatorname{cosec} x=\operatorname{cosec}\left(-\frac{\pi}{4}\right)(\because-\operatorname{cosec}(\theta)=\operatorname{cosec}(-\theta)) \\ \Rightarrow x=-\frac{\pi}{4} \end{array}

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