Question

if A+B = 45° then proove that (1+tanA)(1+tanB)=2​

Answer 1

Here A+B=45

tan(A+B)=tan45

tanA+tanB/1-tanA.tanB=1

tanA+tanB=1-tanA×tanB

tanA+tanB+tanA×tanB=1

adding 1 to both sides

1+tanA+tanB+tanA×tanB=2

1(1+tanA)tanB(1+tanA)=2

(1+tanA)(1+tanB)=2

Hence proved