Find the principal and general solutions of the question $\tan x=\sqrt{3}$.
Find the principal and general solutions of the question $\tan x=\sqrt{3}$.
$\tan x=\sqrt{3}$
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 $n \in Z.$
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