In a triangle `A B C ,` if `A-B=120^0a n dsin(A/2)sin(B/2)sin(C/2)=1/(32),` then the value of `8cosC` is_______

Explanation

To solve the problem, we will follow the steps outlined in the video transcript.

### Step-by-Step Solution:

1. **Given Information**:
We have a triangle \( ABC \) where \( A - B = 120^\circ \) and \( \sin\left(\frac{A}{2}\right) \sin\left(\frac{B}{2}\right) \sin\left(\frac{C}{2}\right) = \frac{1}{32} \).

2. **Using the Product-to-Sum Formulas**:
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