Chapter 12 - Counting and Probability - Section 12.2 Permutations and Combinations - 12.2 Assess Your Understanding - Page 876: 69

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

$sin75^\circ=sin(45^\circ+30^\circ)=sin45^\circ cos30^\circ+cos45^\circ sin30^\circ=(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})+(\frac{\sqrt 2}{2})(\frac{1}{2})=\frac{\sqrt 6+\sqrt 2}{4}$ $cos15^\circ=sin(45^\circ-30^\circ)=cos45^\circ cos30^\circ+sin45^\circ sin30^\circ=(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})+(\frac{\sqrt 2}{2})(\frac{1}{2})=\frac{\sqrt 6+\sqrt 2}{4}$