Question

Rewrite the product using a sum or difference of two functions. cos(π/3) sin(π/4)

a. cos(π/12) - sin(π/12)
b. cos(π/12) + sin(π/12)
c. cos(π/7) - sin(π/6)
d. cos(π/7) + sin(π/6)

Answer 1

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).