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If $A + B = 45 °, then (1 + \tan A) (1 + \tan B)$ is

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answer is C.

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Detailed Solution

$A + B = 45$

$\tan (A + B) = \tan 45$

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

$\tan A + \tan B = 1 - \tan A \tan B$

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

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

$\tan A (1 + \tan B) + 1 (\tan B + 1) = 2$

$(1 + \tan B) (1 + \tan A) = 2$

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