trigonometric product formulas

The Werner formulas are the trigonometric product formulas 2sin α cos β | = | sin(α - β) + sin(α + β) 2cos α cos β | = | cos(α - β) + cos(α + β) 2cos α sin β | = | sin(α + β) - sin(α - β) 2sin α sin β | = | cos(α - β) - cos(α + β). This form of trigonometric functions can be obtained in the Wolfram Language using the command TrigReduce[expr].