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

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$\sec x=2$

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

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

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

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

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