Chapter 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 508: 20

$ -2-\sqrt 3$

$tan\frac{17\pi}{12}=tan(\frac{15\pi}{12}+\frac{4\pi}{12})=tan(\frac{5\pi}{4}+\frac{\pi}{3})=\frac{tan\frac{5\pi}{4}+tan\frac{\pi}{3}}{1-tan\frac{5\pi}{4} tan\frac{\pi}{3}}=\frac{1+\sqrt 3}{1-\sqrt 3}=\frac{1+\sqrt 3}{1-\sqrt 3}\times\frac{1+\sqrt 3}{1+\sqrt 3}=\frac{4+2\sqrt 3}{-2}=-2-\sqrt 3$