If `tanA=x+1andtanB=x-1`, then `x^(2)tan(A-B)` has the value :

Options

A. 1
B. x
C. 0
D. 2

Explanation

To solve the problem where \( \tan A = x + 1 \) and \( \tan B = x - 1 \), we need to find the value of \( x^2 \tan(A - B) \).

### Step-by-Step Solution:

1. **Write down the given equations:**
\[ \tan A = x + 1 \quad \text{(1)} \]
\[ \tan B = x - 1 \quad \text{(2)} \]

2. **Recall the formula for \( \tan(A - B) \):**
\[ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \]

3. **Substitute the values of \( \tan A \) and \( \tan B \) into the formula:**
\[ \tan(A - B) = \frac{(x + 1) - (x - 1)}{1 + (x + 1)(x - 1)} \]

4. **Simplify the numerator:**
\[ \tan(A - B) = \frac{x + 1 - x + 1}{1 + (x^2 - 1)} = \frac{2}{1 + x^2 - 1} = \frac{2}{x^2} \]

5. **Now substitute \( \tan(A - B) \) back into the expression \( x^2 \tan(A - B) \):**
\[ x^2 \tan(A - B) = x^2 \cdot \frac{2}{x^2} \]

6. **Simplify the expression:**
\[ x^2 \tan(A - B) = 2 \]

### Final Answer:
The value of \( x^2 \tan(A - B) \) is \( 2 \).