Question

If a+b = pi by 4 then (1 + tan A )(1+tan B) =

Answer 1

Step-by-step explanation:

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

Hence proved