Use the product-to-sum formulas to write the product as a sum or difference.
sin(x+y) * cos(x-y)
To write the product sin(x+y) * cos(x-y) as a sum or difference, we can use the product-to-sum formulas. These formulas are:
1. sin(A) * cos(B) = (1/2)(sin(A + B) + sin(A - B))
2. cos(A) * cos(B) = (1/2)(cos(A + B) + cos(A - B))
Let's use these formulas to express sin(x+y) * cos(x-y) as a sum or difference:
sin(x+y) * cos(x-y)
= (1/2)(sin((x+y) + (x-y)) + sin((x+y) - (x-y))) [using the product-to-sum formula for sine]
= (1/2)(sin(2x) + sin(2y)) [simplifying the expression]
So, sin(x+y) * cos(x-y) can be written as the sum (1/2)(sin(2x) + sin(2y)).