Question

If `x=tan^(-1)t`, then is`1/x=1/tant`?

Answer 1

`1/x=1/tan^(-1)t`

Explanation:

`1/x=1/tan^(-1)t`

Note that `1/x=x^(-1)` does not mean that `1/x=tant`

as `x=tan^(-1)t` means the angle `x`, whose tangent is `t` and this does not mean that tangent of angle `1/x` is `1/t` or `1/tant` or any other thing apparently similar.

In short, `tan^(-1)t` is different from `1/tant`. The fact is that the latter is `cott`, a ratio, while `x` is an angle, which could be in degrees, radians or even Grads.