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Which of the following expressions is equivalent (sin24°)(cos66°)+(cos24°)(sin66°) to? 2(cos66°)(sin24°)
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. The sine of an angle is equal to the cosine of its 24° 66° complementary angle. Since angles with measures and are sin24° cos66° sin66° complementary to each other, is equal to and is cos24° cos66° sin24° cos24° sin66° equal to . Substituting for and for cos66° cos66° + cos24° cos24° in the given expression yields ^ h^ h ^ h^ h, or cos66° 2+ cos24° 2 ^ h ^ h . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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