Question

If A – B = π /4, then (1 + tan A) (1 – tanB) is equal to 

A. 2 

B. 1 

C. 0 

D. 3

Answer 1

1 = \(\frac{tanA-tanB}{1+tanAtanB}\)

1 + tan A tan B = tan A - tan B 

tan A - tan B - tan A tan B =1 

add both side 1 

1+tan A - tan B - tan A tan B = 1+1 

(1+ tan A)(1+tan B)=2 

Case2: 

put A = 0 AND B = -\(\frac{π}4\)

(1+tan A )(1 - tan A ) = 1× 2