Trigonometry Identities - Sum to Product to Identity (Radians)

Question

Complete the sum to product identity for this expression

$$	ext{cos}{(\frac{3\pi}{4})}-	ext{cos}{(\frac{7\pi}{4})}$$

Accepted Answer

$$=-2 	ext{sin}{( \frac{(\frac{3\pi}{4} + \frac{7\pi}{4})}{2})}   	ext{sin}{( \frac{(\frac{3\pi}{4} - \frac{7\pi}{4})}{2})}$$

Answer

$$=	ext{cos}{( \frac{(\frac{3\pi}{4} + \frac{7\pi}{4})}{2})}  	ext{sin}{( \frac{(\frac{3\pi}{4} + \frac{7\pi}{4})}{2})}$$