Solve the equation (2/arctanx)-arctanx=1

To solve 2/arc tanx -arctanx =
1.

We multiply both sides by arc tanx
.

2 - (arc tanx)^2 = arc
tanx

 2-y^2= y, where y = arc
tanx.

=>  y^2+y-2 =
0.

=> (y-1)(y+2) =
0.

=> y -1 = o, or y+2 =
0.

=> y= 1, or y =
-2.

 y = 1 gives arc tanx = 1. x = tan1 =
1.5574.

y = -2 gives arc tan x = -2. So x = tan (-2) =
2.18504.

Therefore x= 1.5574, or x = 
2.18504.