If `A+B=pi/4`, find the numerical value of (1+tan A)(1+tan B) is equal to

Answer

To solve the problem, we need to find the numerical value of \( (1 + \tan A)(1 + \tan B) \) given that \( A + B = \frac{\pi}{4} \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ A + B = \frac{\pi}{4} \]

2. **Use the tangent addition formula:**
\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Since \( A + B = \frac{\pi}{4} \), we have:
\[ \tan\left(\frac{\pi}{4}\right) = 1 \]
Therefore:
\[ 1 = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]

3. **Cross-multiply to eliminate the fraction:**
\[ 1 - \tan A \tan B = \tan A + \tan B \]

4. **Rearranging the equation:**
\[ 1 = \tan A + \tan B + \tan A \tan B \]

5. **Now, we can express \( (1 + \tan A)(1 + \tan B) \):**
\[ (1 + \tan A)(1 + \tan B) = 1 + \tan A + \tan B + \tan A \tan B \]

6. **Substituting the value from the previous step:**
From step 4, we know that \( \tan A + \tan B + \tan A \tan B = 1 \). Thus:
\[ (1 + \tan A)(1 + \tan B) = 1 + 1 = 2 \]

7. **Final answer:**
\[ (1 + \tan A)(1 + \tan B) = 2 \]

### Summary:
The numerical value of \( (1 + \tan A)(1 + \tan B) \) is \( 2 \).