# Math Help - Prove that

1. ## Prove that

If tanx+tan(x+ pie/3)+tan(x+2pie/3)=3 , then prove that (3tanx -tan^3x)/(1-3tan^2x)=1

2. Originally Posted by matsci0000
If tanx+tan(x+ pie/3)+tan(x+2pie/3)=3 , then prove that (3tanx -tan^3x)/(1-3tan^2x)=1

$3$
= $tanx+tan(x+\frac{\pi}{3})+tan(x+\frac{2\pi}{3})$

= $tanx+\frac{tanx+tan\frac{\pi}{3}}{1-tanx.tan\frac{\pi}{3}}+\frac{tanx+tan\frac{2\pi}{3 }}{1-tanx.tan\frac{2\pi}{3}}$

= $tanx+\frac{tanx+\frac{\sqrt3}{1}}{1-tanx.\frac{\sqrt3}{1}}+\frac{tanx-\frac{\sqrt3}{1}}{1+tanx.\frac{\sqrt3}{1}}$

= $tanx +\frac{8tanx}{1-3tan^2x}$

= $\frac{9tanx-3tan^3x}{1-3tan^2x}$

divide both sides of the equation by 3, you get your answer