Question

A+B=45° (prove that):(1+tan A). (1+tan B) =2​

Answer 1

Proof :

Given, A + B = 45°

Taking tangent to both sides, we get

tan(A + B) = tan45°

⇒ (tanA + tanB)/(1 - tanA tanB) = 1

⇒ tanA + tanB = 1 - tanA tanB

⇒ tanA + tanB + tanA tanB = 1

⇒ 1 + tanA + tanB + tanA tanB = 1 + 1

⇒ 1 (1 + tanA) + tanB (1 + tanA) = 2

⇒ (1 + tanA) (1 + tanB) = 2

Hence, proved.

Answer 2

A+B=45°

tan(A+B)=tan45°

tan A+tan B /1-tan A tan B=1

tan A+ tan B=1-tan A+ tan B

$\boxed{\huge{\bf{ADD\:\:1\:\: BOTH \:\: SIDE}}}$

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

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

$\boxed{\huge{\bf{(1+tan B) (tan A+1}}}$