Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 487: 20

$-2-\sqrt 3$

$tan(\frac{7\pi}{12})=tan(\frac{3\pi}{12}+\frac{4\pi}{12})=tan(\frac{\pi}{4}+\frac{\pi}{3})=\frac{tan(\frac{\pi}{4})+tan(\frac{\pi}{3})}{1-tan(\frac{\pi}{4})tan(\frac{\pi}{3})}=\frac{1+\sqrt 3}{1-(1)(\sqrt 3)}=\frac{1+\sqrt 3}{1-\sqrt 3}\times\frac{1+\sqrt 3}{1+\sqrt 3}=\frac{4+2\sqrt 3}{-2}=-2-\sqrt 3$