Chapter 9 - Trigonometric Identities, Models, and Complex Numbers - 9.3 Sum and Difference Formulas for Sine and Cosine - Exercises and Problems for Section 9.3 - Exercises and Problems - Page 368: 11

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

Finding the exact value using the Laws of Trigonometry, we obtain: $$\sin \left(45^{\circ \:}+60^{\circ \:}\right) \\ \sin \left(45^{\circ \:}\right)\cos \left(60^{\circ \:}\right)+\cos \left(45^{\circ \:}\right)\sin \left(60^{\circ \:}\right) \\ \frac{\sqrt{2}+\sqrt{6}}{4}$$