Sections:

Trigonometric Identities and Equations, Page 10

Product-Sum and Sum-Product Identities

The Product-Sum Identities and the Sum-Product Identities, below, allow you to change addition trigonometric expressions into multiplication trigonometric expressions and vice versa.


Product-Sum Identities

sinα cosβ = 1/2 [sin(α + β) + sin(α - β)]; cosα sinβ = 1/2 [sin(α + β) - sin(α - β)]; sinα sinβ = 1/2 [cos(α - β) - cos(α + β)]; cosα cosβ = 1/2 [cos(α + β) + cos(α - β)]

Sum-Product Identities

sinα + sinβ = 2sin[(α + β)/2] cos[(α - β)/2]; sinα - sinβ = 2cos[(α + β)/2] sin[(α - β)/2]; cosα + cosβ = 2cos[(α + β)/2] cos[(α - β)/2]; cosα - cosβ = -2sin[(α + β)/2] sin[(α - β)/2]