If A + B = 45°, then (1 + tanA)(1 + tanB) = ?

Correct option is C

Given:

​$$A + B = 45^\circ$$​​

Formula Used:

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

$$\tan 45^\circ = 1$$​​​

Solution:

$$\tan 45^\circ = \frac{\tan A + \tan B}{1 - \tan A \tan B}$$

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

tan A + tan B + tan A tan B = 1

Now,

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

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

Thus, the value of (1 + tan A)(1 + tan B) is 2.