આપેલ સમીકરણના મુખ્ય અને વ્યાપક ઉકેલ શોધો : $\tan x=\sqrt{3}$.

$\tan x=\sqrt{3}$

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

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

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