Question

Find principal and general solution of the equation $\tan x=\sqrt{3}$.

Answer 1

$\tan x=\sqrt{3}$

We know,

$\tan \frac{\pi }{3}=\sqrt{3}$

$\tan \frac{4\pi }{3}=\tan (\pi +\frac{\pi }{3})=\tan \frac{\pi }{3}=\sqrt{3}$

Therefore, the principal solutions are $x=\frac{\pi }{3},\frac{4\pi }{3}$.

Now,

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

$x=n\pi +\frac{\pi }{3}$, where $n\in Z$

Therefore, the general solution is

$x=n\pi +\frac{\pi }{3}$, where $n\in Z$