Question

If a-b=π÷4 , then find (1+tanA) (1-tanB)

Answer 1

Tan(A-B)= tan pi/4 = 1
So [ tan A - tan B] = [ 1 + tan A tan B ]

So LHS = tan A - tan B + 1 - tan A tan B
= 1+ tan A tan B + 1 - tan A tan B
= 2

Answer 2

Here ,
        a - b = π/4
take both sides tan 
       tan(a - b) = tanπ/4
(tana - tanb)/(1 + tana.tanb) = 1
tana + tanb = 1 +tana.tanb
tana +tanb +tana.tanb + 1 = 2
(tana +1)(tanb +1) = 2