alleryStart learning →Which expansion is the sum formula for cosine?
Acos a cos b + sin a sin b
Bsin a cos b + cos a sin b
Csin a cos b - cos a sin b
Dcos a cos b - sin a sin b
Answer & Solution
Correct answer: D. cos a cos b - sin a sin b
1. The cosine of a sum equals the product of the cosines minus the product of the sines.
2. In symbols that is cos(a + b) = cos a cos b - sin a sin b.
3. The version with a plus sign is the difference formula for cosine, not the sum formula.
4. The two options that mix sine with cosine are the sine formulas and belong to a different family.
_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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