Can we say that tan-1(x) = cot(X)? As tan-1(x)=1/tan(x)=cot (x)

Cot, is not Tan inverse, which is admittedly confusing. I mean it sounds like it should be its inverse, just from its name, but its not. Tan is defined as sin(x)/cos(x), while Cot is cos(x)/sin(x). Now again, this might make them seem like they are inverses, but they are not and just to prove it to you lets to a little bit of a mathematical expiriment. So if Tan and Cot were inverses, when combined they should cancel each other so. So try taking the Cot(pi/4) and plugging than into Tan (Meaning take cos(pi/4)/sin(pi/4) and plug that into sin(x)/cos(x))

Here"-1"doesnot refers to numerical"-1",but it refers to inverse function.Here tan-1(x) denotes angle or real number.