# How do you solve Tan 2x - tan x=0?

Apr 16, 2015

In this way:

$\tan 2 x = \tan x$ and two tangents are equal if their argument are equal with the moltiplicity.

So:

$2 x = x + k \pi \Rightarrow x = k \pi$

acceptable because we have to remember that for the existence of the function tangent the argument has to be not $\frac{\pi}{2} + k \pi$,

so:

$2 x \ne \frac{\pi}{2} + k \pi \Rightarrow x \ne \frac{\pi}{4} + k \frac{\pi}{2}$

and

$x \ne \frac{\pi}{2} + k \pi$.