If in ` A B C ,A C` is double of `A B` , then the value of `cot(A/2)cot((B-C)/2)` is equal to `1/3` (b) `-1/3` (c) `3` (d) `1/2`

Explanation

To solve the problem, we need to find the value of \( \cot\left(\frac{A}{2}\right) \cot\left(\frac{B-C}{2}\right) \) given that \( AC \) is double of \( AB \) in triangle \( ABC \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that \( AC = 2 \cdot AB \). Let's denote \( AB = c \), \( BC = a \), and \( AC = b \). According to the problem, we have:
\[
b = 2c
...