Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 38

$sin(45^{\circ}+\theta) = \frac{\sqrt{2}}{2}~(cos~\theta+ sin~\theta)$

$sin(45^{\circ}+\theta) = sin(45^{\circ})~cos~\theta+ cos(45^{\circ})~sin~\theta$ $sin(45^{\circ}+\theta) = \frac{\sqrt{2}}{2}~cos~\theta+ \frac{\sqrt{2}}{2}~sin~\theta$ $sin(45^{\circ}+\theta) = \frac{\sqrt{2}}{2}~(cos~\theta+ sin~\theta)$