Final answer:
The value of cos121° cos 7° - sin 121° sin 59° is found using the cosine sum/difference identity, resulting in cos(114°).
Step-by-step explanation:
The student asked to determine the exact value of cos121° cos 7° - sin 121° sin 59°. This expression can be simplified using the trigonometric identity for the cosine of a sum or difference of two angles: cos(A ± B) = cos A cos B ± sin A sin B. In this case, we apply the identity to find the cosine of the difference between 121° and 7°, which is the angle 114°.
Hence, the exact value of our initial expression can be found by calculating cos(121° - 7°), which equals cos(114°).