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Find the principal values of the following: $cosec^{-1} (2) $

$\begin{array}{1 1} -\frac{\pi}{6} \\ \frac{\pi}{2} \\ -\frac{\pi}{2} \\ \frac{\pi}{6} \end{array} $

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  • The range of the principal value of $\; cosec^{-1}x$ is $\left [ \large-\frac{\pi}{2}, \large\frac{\pi}{2} \right ] -${$0$}
Let $cosec^{-1}2 = x \Rightarrow cosec (x) = 2$
We know the range of the principal value of $\; cosec^{-1}x$ is $\left [ \large-\frac{\pi}{2}, \large\frac{\pi}{2} \right ] -${$0$}
Therefore, $cosec (x) = 2 = cosec \large\frac{\pi}{6}$
$\Rightarrow x=\large\frac{\pi}{6}$, where $x \;\epsilon\;$ $\left [ \large-\frac{\pi}{2}, \large\frac{\pi}{2} \right ] -${$0$}
Hence the principal value of $\; cosec^{-1}2$ is $\large\frac{\pi}{6}$

 

answered Mar 2, 2013 by balaji.thirumalai
edited Mar 15, 2013 by thanvigandhi_1
 
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