Question

If A + B = п/4 then ( 1 + tan A ) ( 1+ tan B )

Answer 1

Answer:

Applying tan for the the equation A+B=45

We get...

Tan(A+B)= tan 45°

Where tan (A+B) = tan A +tanB/1-tan A tan B

Therefore,

Tan A +tan B/ 1-tanA tanB=1. (Since tan45°= 1)

TanA+ tan B=1– tanAtanB

TanA+TanB+Tan A TanB=1

TanA+TanB(1+TanA) = 1

Now adding one on both sides...

1+tanA+ Tan B ( Tan A+1)= 1+1

(TanA+1)(1+tanB) = 2

Therefore the answer is 2