Question

if A+B =pi/4, prove that (1+tanA)(1+tanB)=2​

Answer 1

Answer: we have,

A + B = π/4

Taking tan both sides

tan(A+B) = tanπ/4

tan A + tan B/ 1- tan A tanB = 1

tanA + tan B = 1- tanA tanB

tan A + tanB + tanAtanB = 1

Adding 1 both sides.

1 + tan A +tanB + tanA tanB = 2

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

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

Answer 2

Answer:

See the picture for answer