Question

if A+B=45degree so prove that (1+tanA)(1+tanB)=2

Answer 1

Given A+B=45

Take tan on both sides.

Tan(A+B)=Tan(45)

(TanA + TanB) / 1-TanATanB = 1

Tan A + Tan B = 1 - TanATanB

TanA + TanB + TanATanB = 1

Adding 1 on both sides

1+tanA+tanB+tanAtanB=1+1

1+tanA+tanB+tanAtanB=2

1(1+tanA) + tanB(1+tanA)=2

(1+tanA)(1+tanB)=2

Hence proved

Answer 2

this is the way to solve the question.