Question

Which identity is used for the product of sine and cosine?

Options

• \(\sin A\cos B = \sin(A+B)-\sin(A-B)\)

• \(\sin A\cos B = \frac{1}{2}[\sin(A-B)-\sin(A+B)]\)

• \(\sin A\cos B = \frac{1}{2}[\sin(A+B)+\sin(A-B)]\)

• \(\sin A\cos B = \frac{1}{2}[\cos(A+B)+\cos(A-B)]\)

Answer 1

The product-to-sum identity converts a product of sine and cosine into a sum or difference of sine terms. This makes the expression easier to integrate term by term.