OG详解-OG7 数学1 Q45

Choice C is correct. The sine of an angle is equal to the cosine of its complementary angle. Since angles with measures 24° and 66° are complementary to each other, sin24° is equal to cos66° and sin66° is equal to cos24°. Substituting cos66° for sin24° and cos24° for sin66° in the given expression yields (cos66°)(cos66°)+(cos24°)(cos24°), or (cos66°)² +(cos24°)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.