Final answer:
The question requires using the product-to-sum formula to convert a trigonometric product into a sum or difference, a skill typically covered in high school trigonometry classes. The specific expression was not provided, but a hypothetical example using cos(A)sin(B) was used to demonstrate the concept.
Step-by-step explanation:
The student's question involves converting a product of trigonometric functions into a sum or difference using the product-to-sum formulas, which is a topic in high school mathematics, specifically within trigonometry. Unfortunately, the question does not provide the specific trigonometric expression that needs conversion. However, we can illustrate with a general example:
If we have an expression such as cos(A)sin(B), we can use the product-to-sum formula:
cos(A)sin(B) = \(rac{1}{2}[sin(A + B) - sin(A - B)]\)
The expression is now represented as the difference of two sine functions, which is easier to work with in many mathematical analyses.
To simplify further, you need to substitute the specific values of A and B (if given) into the new expression and calculate the sine of the resulting angles. This simplification process may include combining terms, applying identities, or factorizing, depending on the specific expression given.
Always remember to eliminate terms where possible to simplify the algebra and check the answer for reasonableness once you've finished your calculations.