The video explains how to derive the Product-to-Sum Formulas for Sine and Cosine using the Addition and Subtraction Formulas.

sin⁡α sin⁡β=1/2 (cos⁡(α-β)-cos⁡(α+β) )
cos⁡α cos⁡β=1/2 (cos⁡(α-β)+cos⁡(α+β) )
sin⁡α cos⁡β=1/2 (sin⁡(α+β)+sin⁡(α-β) )
cos⁡α sin⁡β=1/2 (sin⁡(α+β)-sin⁡(α-β) )