Question:
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:
To Find: The Principle value of $\operatorname{cosec}^{-1}(2)$
Let the principle value be given by $x$
Now, let $x=\operatorname{cosec}^{-1}(2)$
$\Rightarrow \operatorname{cosec} x=2$
$\Rightarrow \operatorname{cosec} x=\operatorname{cosec}\left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{6}\right)=2\right)$
$\Rightarrow x=\frac{\pi}{6}$
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