Question

if A+B=45 degree.show that {1+tanA}{1+tanB}=2

Answer 1

A+B=45

B=45-A----(1)
lhs = (1+tanA)(1+tanB)

= (1+tanA) [1+ tan(45-A)] from (1)
=(1+tanA)[1+(tan 45-tanA)/(1+tan45tanA)] using tan(X-Y) formula
= (1+tanA)[1+(1-tanA)/(1+tanA)]

= (1+tanA)[(1+tanA+1-tanA)/(1+tanA)]

after cancellation
= 1+tanA+1-tanA
= 2
rhs