How would I write this as a sum or difference?

Question

Cos x/2 cos 3x/2

I know I would use one of the products to sum or sum to product formulas. however I don't know which one to use nor how I would use it in this problem. Thank you.

Answer 1

Product to Sum

x / 2 = (u - v) / 2

3x / 2 = (u + v) / 2

x = u - v

3x = u + v

4x = 2u

2x = u

x = v

cos (x/2) cos (3x/2) = (0.5)(2)[cos (u - v)/2][cos (u + v)/2]

cos (x/2) cos (3x/2) = (0.5)[cos (u - v)/2 + cos (u + v)/2]

cos (x/2) cos (3x/2) = (0.5)[cos u + cos v]

cos (x/2) cos (3x/2) = (0.5)[cos 2x + cos x]