In a `DeltaABC,(a+c)/(a-c)tan(B/2)` is equal to

Options

A. `tan(B/2+C)`
B. `tan(B+C/2)`
C. `cot(B/2+C)`
D. none of these

Explanation

To solve the problem, we need to evaluate the expression \(\frac{A + C}{A - C} \tan\left(\frac{B}{2}\right)\) in triangle \(ABC\).

### Step-by-Step Solution:

1. **Use the Sine Rule**:
The sine rule states that:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = K
...