Question

How do you write an algebraic expression that is equivalent to `cot(arctanx)`?

Answer 1

This expression can be written as

`cot(arctanx)=1/x`

See explanation.

Explanation:

First we can use the identity:

`cot alpha=1/tan alpha`

So we get:

`cot(arctanx)=1/tan(arctanx)`

Now we can simplify the denominator to `x` because `tan` and `cot` are inverse functions and for two inverse functions we can write that:

`f(f^-1(x))=f^-1(f(x))=x`

So after all transformations we get:

`cot(arctanx)=1/x`