What is the difference between arctan and inverse tan?

Hello,

It is not the same function.

arctan (tan (x)) = x

1/tan (x) * tan (x) = 1

in the file jointed,

arctan x is in blue

1/tan x in red.

The arc tangent of x is defined as the inverse tangent function of x when x is real. When the tangent of y is equal to x. Then the arc tangent of x is equal to the inverse tangent function of x, which is equal to y. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarifications