Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 487: 19

$\frac{\sqrt 2-\sqrt 6}{4}$

$cos(\frac{7\pi}{12})=cos(\frac{3\pi}{12}+\frac{4\pi}{12})=cos(\frac{\pi}{4}+\frac{\pi}{3})=cos(\frac{\pi}{4})cos(\frac{\pi}{3})-sin(\frac{\pi}{4})sin(\frac{\pi}{3})=(\frac{\sqrt 2}{2})(\frac{1}{2})-(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})=\frac{\sqrt 2-\sqrt 6}{4}$