Question

Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]

Answer 1

We have:

\[\sqrt{3} \sec x = 2\]
⇒ \[\sec x = \frac{2}{\sqrt{3}}\] (or) 

\[\cos x = \frac{\sqrt{3}}{2}\]

The value of x satisfying \[\cos x = \frac{\sqrt{3}}{2}\] is \[\frac{\pi}{6}\].

∴ \[\cos x = \frac{\sqrt{3}}{2}\]

⇒ \[\cos x = \cos\frac{\pi}{6}\]

⇒ \[x = 2n\pi \pm \frac{\pi}{6}\],

\[n \in Z\]