Question

If A + B = 225°, then the value of (1 + tan A)

(1 + tan B) is

Answer 1

given,
A+B = 225
apply tan on both sides
=> tan(A+B) = tan225
=> tanA+tanB/1-tanAtanB = tan(270-45)
=> tanA+tanB/1-tanAtanB = tan45
=> tanA+tanB/1-tanAtanB = 1
=> tanA+tanB = 1-tanAtanB
=> tanA+tanB+tanAtanB=1
adding 1 on both sides
=> tanA+tanB+tanAtanB+1 = 1+1
=> tanA+tanAtanB+tanB+1 = 2
=> tanA(1+tanB)+(1+tanB) = 2
=> (1+tanB) (1+tanA) = 2

I hope u understand
pls mark it as brainliest answer

Answer 2

Let's Do Different☺️:-


Now,

A+B=225°

so,

tan(A+B)=tan225°

=>tanA+tanB/1-tanA.tanB=tan(180+tan45)

=>tanA+tanB/1-tanA.tanB=>tan180+tan45/1+tan180.tan45

=>Equating LHS and RHS,

Tan A + Tan B= 1 − Tan A Tan B;

=> Tan A + Tan B + Tan A Tan B=1;

=> Tan A + Tan B + Tan A Tan B + 1= 1+1; {adding 1 on both the sides}

so, tanA + tanB=2

Hope My Answer Will Help You☺️