Trigonometry Identities - Product to Sum to Identity (Radians)

Question

Complete the product to sum identity for this expression

$$	ext{cos}{(\frac{7\pi}{4})}	ext{cos}{(\frac{5\pi}{3})}$$

Accepted Answer

$$=\frac{1}{2} \left[   	ext{cos}(\frac{7\pi}{4} - \frac{5\pi}{3}) +  	ext{cos}(\frac{7\pi}{4} + \frac{5\pi}{3})  ight]$$

Answer

$$=\frac{1}{2} \left[   	ext{sin}(\frac{7\pi}{4} + \frac{5\pi}{3}) +  	ext{sin}(\frac{7\pi}{4} - \frac{5\pi}{3})  ight]$$