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caylus
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.

Ver imagen caylus
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