Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 693: 38

$\sin 225^{o}+\sin 55^{o}$

Product-to-Sum: $\displaystyle \cos A\sin B=\frac{1}{2}[\sin(A+B)-\sin(A-B)]$ ---------------- $2\cos 85^{o}\sin 140^{o}=$ $=2(\displaystyle \frac{1}{2}[\sin(85^{o}+140^{o})-\sin(85^{o}-140^{o})])$ $=\sin 225^{o}-\sin(-55^{o})$ $=\sin 225^{o}+\sin 55^{o}$