Find the general solution of each of the following equations:

To Find: General solution.

Given: $\tan ^{3} x-3 \tan x=0 \Rightarrow \tan x\left(\tan ^{2} x-3\right)=0 \Rightarrow \tan x=0$ or $\tan x=\pm \sqrt{3}$

$\Rightarrow \tan x=0$ or $\tan x=\tan \left(\frac{\pi}{3}\right)$ or $\tan x=\tan \left(\frac{2 \pi}{3}\right)$

$\Rightarrow$ Formula used: $\tan \theta=0 \Rightarrow \theta=\mathrm{n} \pi, \mathrm{n} \in I, \tan \theta=\tan \alpha \Rightarrow \theta=\mathrm{k} \pi \pm \alpha, \mathrm{k} \in I$

So $x=n \pi$ or $x=k \pi+\frac{\pi}{3}$ or $x=p \pi+\frac{2 \pi}{3}$ where $n, k, p \in I$

So general solution is $x=n \pi$ or $x=k \pi+\frac{\pi}{3}$ or $x=p \pi+\frac{2 \pi}{3}$ where $n, k, p \in$ ।