Question

Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]

Answer 1

We have:

\[cosecx = - \sqrt{2}\] (or) 

\[\sin x = - \frac{1}{\sqrt{2}}\]
The value of x satisfying 

\[\sin x = - \frac{1}{\sqrt{2}}\] is \[- \frac{\pi}{4}\]

∴ \[\sin x = - \frac{1}{\sqrt{2}}\]

⇒ \[\sin x = \sin ( - \frac{\pi}{4})\]

⇒ \[x = n\pi + \left( - 1 \right)^n \left( - \frac{\pi}{4} \right)\]

 

\[n \in Z\]

⇒ \[x = n\pi + ( - 1 )^{n + 1} \frac{\pi}{4}, n \in Z\]