If A+B=
Question:

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

Solution:

Since $A+B=\frac{\pi}{4}$

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

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

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

i. e. $\tan A+\tan B=1-\tan A \tan B$

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

i. e. $\tan A+1+\tan B(1+\tan A)=1+1$

i. e. $(1+\tan A)(1+\tan B)=2$

Hence, value of $(1+\tan A)(1+\tan B)=2$.

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