MATHHHHHHHHH

Your concept is not correct

y = tan ^(-1) x means the per-image of tan x

For example, if x is 1, then y = π/4

On the other hand, y = cot x = 1/tanx

For example, if x is π/3, then y = √3

So, tan ^(-1) x =/= cot x

For typing, tan ^(-1) x is often written as arctanx

Hope this explaination will help.