Question 67

If $$A + B = 45^\circ$$, then the value of $$2(1 + \tan A)(1 + \tan B)$$ is:

Solution

$$A + B = 45^\circ$$

On taking tan both sides,

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

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

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

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

Now,

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

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

from the eq(1),

= $$2(1 + 1)$$

= 4

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