If sin (A + B) = 1 and cos (A - B) = √3/2, where A and B are acute angles, then find A and B.
Correct: A
From sin (A + B) = 1, we know that sin 90° = 1. So, A + B = 90° --- (Equation 1).
From cos (A - B) = √3/2, we know that cos 30° = √3/2. So, A - B = 30° --- (Equation 2).
Add Equation 1 and Equation 2:
(A + B) + (A - B) = 90° + 30°
2A = 120°
A = 60°.
Substitute A = 60° into Equation 1:
60° + B = 90°
B = 90° - 60°
B = 30°.
Thus, A = 60° and B = 30°.