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

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Detailed Solution

$A + B = 45 °$

Apply $\tan$ on both sides

$\tan (A + B) = \tan 45 °$

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

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

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

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

$∴$ $(1 + \tan A) (1 + \tan B) = 2$

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