Trigonmetry is fun

Geometry Level 2

If A+B=π4A+B = \frac{\pi}4 , find the value of (1+tanA)(1+tanB) (1 +\tan A )(1 +\tan B ) .

Note: A,Bπ2+πnA,B\ne \frac\pi2 + \pi n for integer nn.

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