Question

Complete the product to sum formula.

Answer 1

`(1)/(2)[sin(x+y)+sin(x-y)]`

Explanation:

we know that

To write the products of cosines and sines as sums, we use the following identity, which is called product-to-sum formula:

`cos(A)sin(B)=(1)/(2)[sin(A+B)+sin(A-B)]`

In this problem we have

`cos(x)sin(y)`

therefore

`cos(x)sin(y)=(1)/(2)[sin(x+y)+sin(x-y)]`