Max value of (Tan A - Tan B) has to be found out
But before that i must tell u that the answers that have been given
by other GoIIT ians are also correct if for Max. value =

But I can give u the solution for minimum value.
So first as we know that Tan(A-B) = TanA - TanB
1 +TanA . TanB
TanA- TanB = Tan (A -B) * 1 + TanA.TanB
Now dividing And multiplying by (A-B)
We will get
Tan A - Tan B
=Tan(A-B) * (A-B) * (1 + TanA.TanB)
(A-B)
We know that Tan x = 1
x
So
Min value will be obtained if the function tends to A
As Tan curve is increasing and will get minimum value
When the desired condition can be taken as A almost equal to B but greater
This will give Tan A =Tan B
= (A-B) * (1 + TanA.TanB)
=(A-B) * (1 + Tan2A)
=(A-B) * (Sec2A)
= (A-B) / Cos2A
This is IIT roorkhee Question
plZ rate me for my efforts
Cheers !!!!!!!!!!!!!!!!!!!!!!
