alleryStart learning →Which expression equals cos a cos b?
A(1/2)[cos(a - b) - cos(a + b)]
B(1/2)[cos(a - b) + cos(a + b)]
C(1/2)[sin(a + b) + sin(a - b)]
D(1/2)[cos(a + b) - cos(a - b)]
Answer & Solution
Correct answer: B. (1/2)[cos(a - b) + cos(a + b)]
1. Adding the cosine sum and difference formulas gives 2 cos a cos b = cos(a - b) + cos(a + b).
2. Dividing by 2 gives cos a cos b = (1/2)[cos(a - b) + cos(a + b)].
3. A quick check with a = b = 0 gives 1 on both sides.
4. The option with a minus sign between the cosines equals sin a sin b, which is 0 at a = b = 0 and so fails the check.
_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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