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

Question

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

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Answer

Let $cosec^{-1}\ 2 = x$
Therefore, cosec $x = 2 =cosec \left(\frac{\pi}{6}\right)$
and $cosec \left(\frac{\pi}{6}\right) = 2$
We know that the principle value range of $cosec^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
Therefore, principle value of $cosec^{-1}\ (2)$ is $\frac{\pi}{6}$

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