Simpson's formulas

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by sin α + sin β | = | 2sin[1/2(α + β)] cos[1/2(α - β)] sin α - sin β | = | 2cos[1/2(α + β)] sin[1/2(α - β)] cos α + cos β | = | 2cos[1/2(α + β)] cos[1/2(α - β)] cos α - cos β | = | -2 sin[1/2(α + β)] sin[1/2(α - β)]. This form of trigonometric functions can be obtained in the Wolfram Language using the command TrigFactor[expr].

harmonic addition theorem | trigonometric addition formulas | Werner formulas