Question

Find the principal and general solutions of the following equation.

tan x = $\sqrt{3}$

Answer 1

Here tan x = $\sqrt{3}$, which is positive, so x lies in first or third quadrant.

$\therefore$ tan x = $\sqrt{3}$ = tan ${60}^0$ or tan (180+${60}^0$)

=tan ${60}^0$ or tan ${240}^0$

= tan$\frac{\pi }{3}$ or tan $\frac{4\pi }{3}$

Hence the principal solutions are $\frac{\pi }{3},\frac{4\pi }{3}$.

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

$\Rightarrow x=n\pi +\frac{\pi }{3}whenenϵZ$.