Quote:

3)Use the compound angle formulas and appropriate angles to find the exact value of $\displaystyle tan(\frac{5\pi}{12})$.

This is what i have done:

$\displaystyle tan(\frac{5\pi}{12}=tan(\pi-\frac{7\pi}{12})$

$\displaystyle =tan(\pi-(\frac{\pi}{3}+\frac{\pi}{4})$

$\displaystyle =\frac{tan(\pi)-tan(\frac{\pi}{3})-tan(\frac{\pi}{4})-tan(\pi)tan(\frac{\pi}{3})tan(\frac{\pi}{4})}{1+ta n(\pi)tan(\frac{\pi}{3})+tan(\pi)tan(\frac{\pi}{4} )+tan(\frac{\pi}{3})tan(\frac{\pi}{4})}$

$\displaystyle =\frac{0-\sqrt3-1-0*\sqrt3*1}{1+0*\sqrt3+0*1+\sqrt3*1}$

$\displaystyle =\frac{\sqrt3-1}{1+\sqrt3}$

book's answer is$\displaystyle 2+\sqrt3$

Multiply your answer by $\displaystyle \frac{1-\sqrt{3}}{1-\sqrt{3}}$ (multiplying the numerator and the denominator by the conjugate of the denominator - it's similar to 'rationalizing the denominator')