Question

tanA= (1-tanB)/(1+tanB) then A+B=?​

Answer 1

Answer:

Okay, let us take this step by step.

First, open up the expression:

(1+tanA)*(1+tanB) = 1 + tanA + tanB + (tanA)*(tanB) = 2 (as mentioned)

=> tanA + tanB = 1 - (tanA)*(tanB) (I skipped a couple of steps here. Basically subtract 1 from both sides, then subtract (tanA)*(tanB) from both sides)

=> (tanA + tanB)/(1 - (tanA)*(tanB)) = 1

We know, tan(A + B) = (tanA + tanB)/1 - (tanA)*(tanB)

=> tan(A+B) = 1

=> tan(A+B) = tan(45 0 ) = tan((pi)/4)

=>A+B = 45 0 = (pi)/4

Answer 2

Answer:

1. tanA=1-tanB/1+tanB
2. tanA+tanA×tanB=1-tanB
3. tanA+tanB=1-tanA×tanB
4. tanA+tanB/1-tanA×tanB=1
5. tan(A+B)=1
6. tan(A+B)=tan45°