## anonymous 5 years ago How do you find 3tan^3x=tanx?

1. anonymous

Simplify both sides with tanx 3tan^2x=1 , tan^2x=1/3 and root both side , $\left| tanx \right|=1/\sqrt{3}$ So go on from here

2. anonymous

thank you!

3. anonymous

No, don't do that. Unless you want to lose half your solutions.

4. anonymous

$3\tan^3x = \tan x \iff \tan x\ (3\tan^2x -1) = 0$ $\implies \tan x = 0 \implies x = ...$ OR $\implies \tan^2x = \frac{1}{3} \implies \tan x = \pm \sqrt{\frac{1}{3}}$