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

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, $\sin 24°$ is equal to $\cos 66°$ and $\sin 66°$ is equal to $\cos 24°$. Substituting $\cos 66°$ for $\sin 24°$ and $\cos 24°$ for $\sin 66°$ in the given expression yields $\left(\cos 66°\right)\left(\cos 66°\right)+\left(\cos 24°\right)\left(\cos 24°\right)$, or ${\left(\cos 66°\right)}^2+{\left(\cos 24°\right)}^2$.

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.