(ii) Convert the products of sine A and cos C into the sum form of trigonometric functions of the triangle above.

To convert the product of $\sin A$ and $\cos C$ into a sum form, we can utilize the product-to-sum identities in trigonometry.

Step 1: Break Down the Problem

We need to express the product $\sin A \cos C$ in terms of the sum of trigonometric functions.

Step 2: Relevant Concepts

The product-to-sum identities state:

$\sin x \cos y = \frac{1}{2} \left( \sin(x+y) + \sin(x-y) \right)$

We will use this identity with $x = A$ and $y = C$.

Step 3: Analysis and Detail

Using the identity:

$\sin A \cos C = \frac{1}{2} \left( \sin(A+C) + \sin(A-C) \right)$

This expression converts the product of $\sin A$ and $\cos C$ into a sum.

Step 4: Verify and Summarize

We have used the correct identity, and the transformation is verified since it follows the derivation of the product-to-sum formulas.

Final Answer

$\sin A \cos C = \frac{1}{2} \left( \sin(A+C) + \sin(A-C) \right)$