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Mark the tick against the correct answer in the following:

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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