The principal value of \(cosec^{-1}(\sqrt{2})\)isA. \(\frac{-\pi}{4}\

1.	The principal value of \(cosec^{-1}(\sqrt{2})\)isA. \(\frac{-\pi}{4}\)B. \(\frac{3\pi}{4}\) C. \(\frac{5\pi}{4}\) D. none of these
Answer» Correct Answer is \(-\frac{\pi}{4}\) Let the principle value be given by x Now, let x = \(cosec^{-1}(\sqrt{2})\) cosec x = \(-\sqrt{2}\) cosec x= - cosec( \(\frac{\pi}{4}\)) (\(\because cosec\left(\frac{\pi}{4}\right)=\sqrt{2}\)) cosec x=cosec( \(-\frac{\pi}{4}\)) ( \(\because -cosec(\theta)=cosec(-\theta\))) x =\(-\frac{\pi}{4}\)

The principal value of \(cosec^{-1}(\sqrt{2})\)isA. \(\frac{-\pi}{4}\)B. \(\frac{3\pi}{4}\) C. \(\frac{5\pi}{4}\) D. none of these

Answer»

Correct Answer is \(-\frac{\pi}{4}\)

Let the principle value be given by x

Now, let x = \(cosec^{-1}(\sqrt{2})\)

cosec x = \(-\sqrt{2}\)

cosec x= - cosec( \(\frac{\pi}{4}\)) (\(\because cosec\left(\frac{\pi}{4}\right)=\sqrt{2}\))

cosec x=cosec( \(-\frac{\pi}{4}\)) ( \(\because -cosec(\theta)=cosec(-\theta\)))

x =\(-\frac{\pi}{4}\)