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Products of Functions

The following formulas relate the products of sines and cosines to sines and cosines of multiple angles. These formulas are derived from the addition formulas. They are useful identities for simplification.

sin(α)sin(β) = - (cos(α + β) - cos(α - β))    

cos(α)cos(β) = (cos(α + β) + cos(α - β))    

sin(α)cos(β) = (sin(α + β) + sin(α - β))    

cos(α)sin(β) = (sin(α + β) - sin(α - β))    

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