# HELP WITH TRIG tan3x (1 Viewer)

#### littlesmallworld

##### Member
Prove for tan 3x= 3tanx-tan^3/1-3tan^2x using sin3x and cos3x

#### myawesome

##### New Member
can you take a pic or use brackets or something.. what is tan^3

#### HeroicPandas

##### Heroic!
$\bg_white Prove that tan3x = \frac{3tanx - tan^3 x}{1-3tan^2x}$

tan^3 = tan3

#### Drongoski

##### Well-Known Member
If allowed to use formula for tan(A+B):

$\bg_white tan3x = tan(x+2x) = \frac {tanx + tan2x}{1-tanx \cdot tan2x} = \frac {tan x + \frac {2tan x}{1-tan^2 x}}{1 - tan x \cdot \frac {2tan x}{1-tan^2 x}} \\ \\ = \cdots = \frac {3tan x - tan^3 x}{1 - 3 tan^2 x}$

Last edited:

#### mahmoudali

##### Member
If allowed to use formula for tan(A+B):

$\bg_white tan3x = tan(x+2x) = \frac {tanx + tan2x}{1-tanx \cdot tan2x} = \frac {tan x + \frac {2tan x}{1-tan^2 x}}{1 - tan x \cdot \frac {2tan x}{1-tan^2 x}} \\ \\ = \cdots = \frac {3tan x - tan^3 x}{1 - 3 tan^2 x}$
question says using $\bg_white \ \ sin(3x)\ \ and\ \ cos(3x)$

#### Drongoski

##### Well-Known Member
question says using $\bg_white \ \ sin(3x)\ \ and\ \ cos(3x)$
Oh thanks. Didn't see that.