alleryStart learning →Which product equals sin a + sin b?
A2 sin((a - b)/2) cos((a + b)/2)
B2 cos((a + b)/2) cos((a - b)/2)
C2 sin((a + b)/2) cos((a - b)/2)
D2 sin((a + b)/2) sin((a - b)/2)
Answer & Solution
Correct answer: C. 2 sin((a + b)/2) cos((a - b)/2)
1. For a sum of sines the sine takes the half sum of the angles and the cosine takes the half difference.
2. So sin a + sin b = 2 sin((a + b)/2) cos((a - b)/2).
3. The option that swaps them is the formula for sin a - sin b.
4. The option built from two cosines is the formula for cos a + cos b.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.4 Sum-to-Product and Product-to-Sum Formulas_
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