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

Explanation

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

### Step 1: Use the tangent addition formula
Since \( A + B = \frac{\pi}{4} \), we can use the tangent addition formula:
\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Substituting \( A + B = \frac{\pi}{4} \) gives:
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