Question

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

Answer 1

Let cosec-1$(2)$ = y.
Then, $cosec \,y =2= cosec \bigg(\frac{\pi}{6}\bigg)$
We know that the range of the principal value branch of cosec-1 is $\bigg[\frac {-\pi}{2},\frac {\pi}{2}\bigg]-\\{0\\}$
Therefore, the principal value of cosec-1$(2) is \,\frac {\pi}{6}$