Question

Find the general solution of the following equation:

\[\sec x = \sqrt{2}\]

Answer 1

We have:
\[\sec x = \sqrt{2}\] (or) 

\[\cos x = \frac{1}{\sqrt{2}}\]

The value of x satisfying \[\cos x = \frac{1}{\sqrt{2}}\] is \[\frac{\pi}{4}\]

∴ \[\cos x = \frac{1}{\sqrt{2}}\]

⇒ \[\cos x = \cos \frac{\pi}{4}\]

⇒ \[x = 2n\pi \pm \frac{\pi}{4}\],

\[n \in Z\]