Which of the following identities correctly rewrites as a product?

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Which of the following identities correctly rewrites

\sin A + \sin B

as a product? (a)

2\sin\dfrac{A-B}{2}\cos\dfrac{A+B}{2}

(b)

2\sin\dfrac{A+B}{2}\cos\dfrac{A-B}{2}

(c)

2\cos\dfrac{A+B}{2}\cos\dfrac{A-B}{2}

(d)

\sin\dfrac{A+B}{2}\cos\dfrac{A-B}{2}