Find the principal solutions of x=-3 - Vidyadip

Question

Find the principal solutions of $\tan x=-\sqrt{3}$

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Answer

$ \tan x=-\sqrt{3}$
$\therefore \tan x=-\tan \left(\frac{\pi}{3}\right)$
$\therefore \tan x=\tan \left(\pi-\frac{\pi}{3}\right)$
$=\tan \left(\frac{2 \pi}{3}\right) \text { and } \tan x=\tan \left(2 \pi-\frac{\pi}{3}\right)$
$=\tan \left(\frac{5 \pi}{3}\right) $
such that $0 \leq \frac{2 \pi}{3}<2 \pi$ and $0 \leq \frac{5 \pi}{3}<2 \pi$
$\therefore$ The required principal solutions are $x=\frac{2 \pi}{3}$ and $x=\frac{5 \pi}{3}$.

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