If `A+B = pi/4`, then prove that `(1+tanA ) (1+tanB)=2`.

Explanation

To prove that if \( A + B = \frac{\pi}{4} \), then \( (1 + \tan A)(1 + \tan B) = 2 \), we can follow these steps:

### Step 1: Use the identity for tangent of a sum
Given \( A + B = \frac{\pi}{4} \), we can use the tangent addition formula:
\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Since \( \tan\left(\frac{\pi}{4}\right) = 1 \), we have:
...