Which of the following expressions is equivalent to sin 24 ° cos 66 ° + cos 24 ° sin 66

Question

Which of the following expressions is equivalent to sin 24 &#176; cos 66 &#176; + cos 24 &#176; sin 66 &#176; ?

Accepted Answer

Choice C is correct. The sine of an angle is equal to the cosine of its complementary angle. Since angles with measures 24 &deg; and 66 &deg; are complementary to each other, sin 24 &deg; is equal to cos 66 &deg; and sin 66 &deg; is equal to cos 24 &deg; . Substituting cos 66 &deg; for sin 24 &deg; and cos 24 &deg; for sin 66 &deg; in the given expression yields cos 66 &deg; cos 66 &deg; + cos 24 &deg; cos 24 &deg; , or cos 66 &deg; 2 + cos 24 &deg; 2 . 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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