The principal value of cosec^-1(-√2) is

Question

The principal value of \(cosec^{-1}(\sqrt{2})\)is

A. \(\frac{-\pi}{4}\)

B. \(\frac{3\pi}{4}\) 

C. \(\frac{5\pi}{4}\) 

D. none of these

Answer 1

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