In triangle `ABC,` if `A-B=120^@ and R=8r,` where `R and r` have their usual meanings, then `cos C` equal (a) `3/4` (b) `2/3` (c) `5/6` (d) `7/8`

Explanation

To solve the problem, we need to find the value of \( \cos C \) in triangle \( ABC \) given that \( A - B = 120^\circ \) and \( R = 8r \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We know that \( R \) is the circumradius and \( r \) is the inradius of triangle \( ABC \). The relationship given is \( R = 8r \).

2. **Using the Formula for Inradius**:
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