The sum and difference formulas of trigonometric functions are as follows: sin α sin β =-[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 .

The formula of product sum and difference is a set of identities of trigonometric function in elementary mathematics. The product and difference formula transforms the product of two trigonometric functions into a constant multiple of the sum of the other two trigonometric functions, thus reducing the order. Formula: product and difference are sum and difference, and cosine should be added later; Synonym function takes sine, and sine multiplication takes negative sign. Historically, before logarithm appeared, multiplication and division were converted into addition and subtraction by multiplication and division formula, and trigonometric function table was needed for operation.