Find the set values of cosec^ -1 ( 3 2 ) - Vidyadip

Question

Find the set values of $\text{cosec}^{-1}\Big(\frac{\sqrt3}{2}\Big)$

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Answer

$\text{cosec}^{-1}\text{x}$ represents an angle in $\Big[-\frac{\pi}{2},0\Big)\cup\Big(0,\frac{\pi}{2}\Big]$whose cosecant is x.

Domain of $\text{cosec}^{-1}\text{x}$ is $(-\infty,-1]\cup[1,\infty)$

$\frac{\sqrt3}{2}\notin(-\infty,-1]\cup[1,\infty)$

Hence, $\text{cosec}^{-1}\Big(\frac{\sqrt3}{2}\Big)$ does not exist or its $\phi.$

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