Question

show that tan(45+A) tan(45-A)=1

Answer 1

tan(x+y ) = (tanx + tan y)/(1- tanx tany)
tan 45 = 1

lhs = tan(45+A)tan(45-A)

= (tan 45 +tan A)/(1- tan45tanA) * (tan45- tanA)/(1+tan45tanA)
= (1+tanA)/(1- tanA) * (1- tanA)/(1+tanA)
after cancellation
=1
RHS