Find the principal values of the following:

    10. \textup{cosec}^{-1}(-\sqrt2)

Answers (1)

Let us assume the value of \textup{cosec}^{-1}(-\sqrt2) = y , then

we have cosec\ y = (-\sqrt 2)   or

 -cosec\ (\frac{\pi}{4}) = (-\sqrt 2) = cosec\ (\frac{-\pi}{4}).

and the range of the principal values of \textup{cosec}^{-1}  lies between  \left [ \frac{-\pi}{2},\frac{\pi}{2} \right ] - \left \{ 0 \right \}.

hence the principal value of \textup{cosec}^{-1}(-\sqrt2) is \frac{-\pi}{4}.

 

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