Originally Posted by

**satis** I'm afraid I'm lost attempting to solve what is probably a really simple problem. The idea is to get an exact answer using the trigonometric difference identity for tangent.

$\displaystyle \tan(\frac{-\pi}{12})$

which is the same as

$\displaystyle \color {red} \tan(\frac{\pi}{3} - \frac{\pi}{4}) \quad $\\edit: $\displaystyle \color {blue} \tan(\frac{\pi}{4}-\frac{\pi}{3})$

the formula is

$\displaystyle \frac{tanA - tanB}{1+tanAtanB}$

thus

$\displaystyle \frac{\tan(\frac{\pi}{3}) - \tan(\frac{\pi}{4})}{1+\tan(\frac{\pi}{3})tan(\fra c{\pi}{4})}$

ergo

$\displaystyle \frac{\sqrt3 - 1}{1+\sqrt3} \quad $ \\edit $\displaystyle \color {blue}\frac{1- \sqrt3}{1+\sqrt3} \quad $

and this is where I'm stuck. The book has the answer as $\displaystyle -2 + \sqrt3$, so either I'm completely wrong, or I just don't know how to simplify properly. Any assistance would be greatly appreciated.