Question

if A - B = π/4 then (1+tanA)(1-tanB) is equals to ??​

Answer 1

Answer:

A-B=π/4

Which implies A=B+π/4

Taking tan on both sides

tanA=tan(B+π/4)

tanA=(tanB + tan(π\4))/(1- tanB.tan(π/4))

tanA=(tanB+1)/(1-tanB)

Substituting the value of tanA in

(1+tanA).(1-tanB) we get

(1+(tanB+1)/(1-tanB)).(1-tanB)

= (1-tanB+tanB+1)/(1-tanB).(1-tanB)

=2