Question

if a+b= pi/4 , prove that (1+tan A) (1+tanB) = 2​

Answer 1

Hello Mate,

Here is your answer,

Given:

a + b = 45°

To find:

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

Solution:

Apply tan on both sides we get,

Tan(a + b) = tan(45°)

TanA + TanB/1- tanA tanB = 1

TanA + tanB = 1 - tanA.tanB

TanA + tanB + tanA.tanB = 1

Add one on both sides,

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

Take (1+ tanA) common we get,

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

Hence proved

Hope it helps:)