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What is the sum and difference formula in advanced mathematics?
Product sum and difference formula:

sinαsinβ=-[cos(α+β)-cos(α-β)]/2

cosαcosβ=[cos(α+β)+cos(α-β)]/2

sinαcosβ=[sin(α+β)+sin(α-β)]/2

cosαsinβ=[sin(α+β)-sin(α-β)]/2

Sum-difference product formula:

sinθ+sinφ= 2 sin[(θ+φ)/2]cos[(θ-φ)/2]

sinθ-sinφ= 2cos[(θ+φ)/2]sin[(θ-φ)/2]

cosθ+cosφ= 2cos[(θ+φ)/2]cos[(θ-φ)/2]

cosθ-cosφ=-2 sin[(θ+φ)/2]sin[(θ-φ)/2]