Find the principal value of cosec ^ -1 (2) - Vidyadip

MCQ

Find the principal value of $cosec ^{-1}(2)$

✓
$\frac{\pi}{6}$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{3}$
D
$0$

✓

Answer

Correct option: A.

$\frac{\pi}{6}$

a
Let $cosec ^{-1}(2)=y$

Then, $cosec y=2=cosec \left(\frac{\pi}{6}\right)$

We know that the range of the principal value branch of $cosec ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$.

Therefore, the principal value of $cosec ^{-1}(2)$ is $\frac{\pi}{6}$

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