if (1-tanx)/1+tanx=tany &x-y=pi/6,thenx=? y=?

Question

1) x=5pi/24 ,y=pi/24
2) x=-7pi/24 ,y=-11pi/24
3) x=-115pi/24 ,y=-119pi/24

Answer 1

LHS=>
(1- tan x) / (1+tan x) = (tan pi/4 - tan x) / (1+ tan pi/4 . tan x)
= tan (pi/4 - x) = tan y
then pi/4 - x = y
=> x+y = pi/4-----(1)
and x-y= pi/6----(2)
so adding (1) and (2), y= 5pi/24
substituting in (1), x= pi/4 - 5pi/24 = pi/24
So I'd say answer number 1)