Question

If A+B =π/4 then prove that (1+ tanA ) (1+ tanB)= 2

Answer 1

Answer:

(1+ tan A) (1+ tan B) = 2

(1+ tan 2 A+B) = 2

1+ ((tan A +tan B / 1 - tan A tan B) 2). =2

1+ (tan (A+B) ) 2 = 2

1+ (tan( pi /4)) 2 =2

1+ (1)2 = 2

1+ 1 =2

2 = 2