Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 693: 41

$3\cos x-3\cos 9x$

Product-to-Sum: $\displaystyle \sin A\sin B=\frac{1}{2}[\cos(A-B)-\cos(A+B)]$ $\cos(-x)=\cos x$ --------- $6\sin 4x\sin 5x=$ $=\displaystyle \frac{6}{2}[\cos(4x-5x)-\cos(4x+5x)]$ $=3[\cos(-x)-\cos(9x)]$ $=3\cos x-3\cos 9x$