Final answer:
To rewrite the product cos(π/3)sin(π/4) using a sum or difference of two functions, we use the identity sin(a)cos(b) = (1/2)(sin(a+b) + sin(a-b)). By substituting the given values into the identity, we find that the correct answer is (a) cos(π/12) - sin(π/12).
Step-by-step explanation:
To rewrite the product using a sum or difference of two functions, let's use the identity sin(a)cos(b) = (1/2)(sin(a+b) + sin(a-b)). In this case, we have cos(π/3)sin(π/4). Let a = π/3 and b = π/4. Substituting these values into the identity, we get:
cos(π/3)sin(π/4) = (1/2)(sin(π/3 + π/4) + sin(π/3 - π/4))
Expanding the sin functions and simplifying, we get:
cos(π/3)sin(π/4) = (1/2)(sin(7π/12) + sin(π/12))
Therefore, the correct answer is (a) cos(π/12) - sin(π/12).