Question

If A + B = π/4 , prove that
(1+tanA) (1+tan B) = 2 ​

Answer 1

Given,

A + B = π/4

To Prove,

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

Solution,

Since, we are given that

A + B = π/4

Taking, tan both sides

tan(A+B) = tan π/4 = 1

(tan A + tan B)/1−tanAtanB = 1

tan A + tan B = 1−tanAtanB

Adding 1 to both sides,

1 + tan A + tan B + tan A tan B=2

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

Hence proved.

Answer 2

Given: A + B = π/4

To find: we have to prove that (1+tanA) (1+tan B) = 2 ​

Solution step by step:

• Here we will take

A + B = π/4

• Taking Tan on both sides

Tan(A + B) = Tan(π/4)

• we have the formula for $tan(A + B) =\dfrac{tan A + tan B}{1- tan A tanB }$

$\dfrac{tan A + tan B}{1- tan A tanB }=1 \\\\tanA + tan B = 1- tanA tanB\\tan A + tanB + tanAtanB = 1$

• Now we will add 1 on both sides

$1+tan A + tanB + tanAtanB = 2\\1(1+tanA)+tabB(1+tanA)=2\\(1+tanA)(1+tanB)=2$

Final answer:

Hence the is proved