# Find the principal and general solutions of the following equations: Q (1)   $\small \tan x = \sqrt{3}$

$\tan x = \sqrt{3}$
We know that the value of    $\tan \frac{\pi}{3} = \sqrt{3}$   and  $\tan \frac{4\pi}{3} = \tan\left (\pi + \frac{\pi}{3} \right ) = \tan\frac{\pi}{3}$ Therefore the principle solution is x = $\frac{\pi}{3} and \frac{4\pi}{3}$

we also know that the value of tan x repeats after an interval of $\pi$
So,  by this, we can say that

$\tan x = \tan \frac{\pi}{3} \Rightarrow x = n\pi + \frac{\pi}{3}$         where n $\epsilon$ Z

therefore, the general solution is x = $n\pi +\frac{\pi}{3}$

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