Find the principal value of cosec^{-1}(2). | vedclass

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Question

(A) Let $cosec^{-1}(2) = y$.Then,$cosec(y) = 2$.We know that $cosec(\frac{\pi}{6}) = 2$.Since the range of the principal value branch of $cosec^{-1}$

Vedclass · Accepted Answer

$\frac{\pi}{6}$

Vedclass · Answer

(A) Let $cosec^{-1}(2) = y$.Then,$cosec(y) = 2$.We know that $cosec(\frac{\pi}{6}) = 2$.Since the range of the principal value branch of $cosec^{-1}$ is $[-\frac{\pi}{2}, \frac{\pi}{2}] - \{0\}$,and $\frac{\pi}{6}$ lies within this interval.Therefore,the principal value of $cosec^{-1}(2)$ is $\frac{\pi}{6}$.

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

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