# Find the principal and general solutions of the equation

Question:

Find the principal and general solutions of the equation

Solution:

$\tan x=\sqrt{3}$

It is known that $\tan \frac{\pi}{3}=\sqrt{3}$ and $\tan \left(\frac{4 \pi}{3}\right)=\tan \left(\pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}=\sqrt{3}$

Therefore, the principal solutions are $x=\frac{\pi}{3}$ and $\frac{4 \pi}{3}$.

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

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

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