Question

A+B=225°
prove that ..
(1+tanA)(1+tanB) = 2
​

Answer 1

Answer:

A+B=225;

Taking tangent of the angles, we get

Tan(A+B)=Tan(225)=Tan(180°+45°);

LHS:

Tan(A + B) = (Tan A + Tan B)/(1 − Tan A Tan B);

RHS:

Tan(180°+45°)=(Tan180°+Tan45°)/(1-Tan180°.Tan45°);

**** Tan180°=0 & Tan45°=1****

> Tan(225°)=1;

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}

After factorisation,

(1+TanA)(1+TanB)=2