Question

If a+b=45°
Prove that (1+tan a)(1+tanb)=2

Answer 1

a+b =45 then a=45and b=0 then (1+tan45)(1+tan0) so tan 45 is 1 then (1+1)(1)=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

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