Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 288: 10

$\sin75^{\circ} =(\frac{\sqrt 6 + \sqrt 2}{4})$

$\sin75^{\circ}$ = $sin(A−B)=sin(A)cos(B)−cos(A)sin(B)$ $sin(120−45)=sin(120)cos(45)−cos(120)sin(45)$ $\sin75^{\circ} =(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})-(\frac{-1}{2})(\frac{\sqrt 2}{2})$ $\sin75^{\circ} =(\frac{\sqrt 6}{4})+(\frac{\sqrt 2}{4})$ $\sin75^{\circ} =(\frac{\sqrt 6 + \sqrt 2}{4})$