alleryStart learning →Expand sin(a + b) with the sum formula for sine.
Asin a cos b + cos a sin b
Bsin a cos b - cos a sin b
Csin a sin b + cos a cos b
Dcos a cos b - sin a sin b
Answer & Solution
Correct answer: A. sin a cos b + cos a sin b
1. The sine of a sum equals the sine of the first angle times the cosine of the second, plus the cosine of the first times the sine of the second.
2. In symbols that is sin(a + b) = sin a cos b + cos a sin b.
3. The same product with a minus sign is the difference formula for sine.
4. The two options built from like functions are the cosine formulas, so neither expands a sine.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.2 Sum and Difference Identities_
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