Solution:
Given that:
To evaluate sin (A+B) and sin (A-B),
Step 1: Express the compound angle formula.
According to the compound angle formula,
Step 2: Evaluate cos (B) and sin (A).
According to the Pythagorean identities,
Thus,
Similarly,
Step 3: Evaluate sin (A+B).
Recall,
Step 4: Evaluate sin(A-B).
Recall,
Hence, we have