Question: Find the principal value of \begin{align} cosec^{-1}\left({2}\right)\end{align}

Answer:

\begin{align} Let \;\; cosec^{-1}\left({2}\right)=y \;\;Then\;\; cosec y = 2 = cosec\left(\frac{\pi}{6}\right)\end{align}

We know that the range of the principal value branch of cosec−1 is

\begin{align} \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - \left(0 \right). \end{align}

Therefore, the principal value of

\begin{align} \frac{\pi}{6}\end{align}

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Question: Find the principal value of \begin{align} cosec^{-1}\left({2}\right)\end{align}

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