Question

If A+B=45°then prove that (1+tan A)(1+tanB)=2​

Answer 1

{Take tan on both the sides }

tan(A+B) = tan45

tanA+tanB/1- tanA tanB = 1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

adding "1" on both sides

1+ tanA+tanB+tanA.tanB=1+1

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

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

 Hence proved .

Answer 2

Answer:

Given A+B=45

{Take tan on both the sides }

tan(A+B) = tan45

tanA+tanB/1- tanA tanB = 1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

adding "1" on both sides

1+ tanA+tanB+tanA.tanB=1+1

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

(1+tanA)(1+tanB)=2 Hence proved .