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Mark the tick against the correct answer in the following: The principal value of \operatorname{cosec}^{-1}(2) is
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{2 \pi}{3}
D. \frac{5 \pi}{6}
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}(2) is
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{2 \pi}{3}
D. \frac{5 \pi}{6}

Solution:

Option(B) is correct.
To Find: The Principle value of \operatorname{cosec}^{-1}(2)
Let the principle value be given by x
Now, let x=\operatorname{cosec}^{-1}(2)
\begin{array}{l} \Rightarrow \operatorname{cosec} x=2 \\ \Rightarrow \operatorname{cosec} x=\operatorname{cosec}\left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{6}\right)=2\right) \\ \Rightarrow x=\frac{\pi}{6} \end{array}

i

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