sin(A+B)=sinAcosB+cosAsinB .

tan(A+B)=(tanA+tanB)/( 1-tanA tanB).

tan(A-B)=(tanA-tanB)/( 1+tanA tanB).

sin5x * sinx =(- 1/2)(cos6x-cos4x).

sinαsinβ=- 1/2[cos(α+β)-cos(α-β)].

cosαcosβ= 1/2[cos(α+β)+cos(α-β)].

definition

Product is the name of many different concepts in mathematics. In arithmetic, the result of multiplication of two or more numbers is called their product or product. When the multiplied numbers are real numbers or complex numbers, the order of multiplication has no effect on the product, which is called commutativity. When the product is a quaternion or matrix, or an element in some algebraic structures, the order will affect the result of the product. This shows that the multiplication of these objects is not commutative.