If A + B = 4 , then (1 + A)(1 + B) = - Vidyadip

MCQ

If $A + B = \frac{\pi }{4},$ then $(1 + \tan A)(1 + \tan B) = $

A
$1$
✓
$2$
C
$\infty $
D
$-2$

✓

Answer

Correct option: B.

$2$

b
(b) Given that $A + B = \frac{\pi }{4}\,$

$\Rightarrow \,\tan \,(A + B) = \tan \,\frac{\pi }{4}$

$ \Rightarrow \,\,\frac{{\tan A + \tan B}}{{1 - \tan A\,\tan B}} = 1$

$ \Rightarrow \,\,\tan A + \tan B + \tan A\,\tan B = 1$

$ \Rightarrow \,\,(1 + \tan A)\,(1 + \tan B) = 2$.

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