Find the principal and general solutions of the equation $sec x=2$

$\sec x=2$

It is known that $\sec \frac{\pi}{3}=2$ and $\sec \frac{5 \pi}{3}=\sec \left(2 \pi-\frac{\pi}{3}\right)=\sec \frac{\pi}{3}=2$

Therefore, the principal solutions are $x=\frac{\pi}{3}$ and $\frac{5 \pi}{3}$

Now, $\sec x=\sec \frac{\pi}{3}$

$\Rightarrow \cos x=\cos \frac{\pi}{3} \quad\left[\sec x=\frac{1}{\cos x}\right]$

$\Rightarrow \mathrm{x}=2 \mathrm{n} \pi \pm \frac{\pi}{3}$, where $\mathrm{n} \in \mathrm{Z}$

Therefore, the general solution is $\mathrm{x}=2 \mathrm{n} \pi \pm \frac{\pi}{3}$, where $n \in \mathbf{Z}$