Krishna
0

Step 1: Calculate the values of the inverse function.


                  GIVEN: \cosec^{-1}(-\sqrt{2})


                Let   \cosec^{-1}(-\sqrt{2}) = y

                                                             Where \frac{-\pi}{2} < y < \frac{-\pi}{2}         

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


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

                

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


                          y = - \frac{\pi}{4}


\therefore \text{The principal value of the} \cosec (\sqrt{2}) \text{ is } \frac{-\pi}{4}