Question

How do you verify `(1+tan x) / (1+cot x) = 2`?

Answer 1

It is not possible to verify #(1+tan(x))/(1+cot(x)) = 2
because it isn't (in general) true.

Explanation:

As an obvious counter example consider the case when `x=pi/4`.

`color(white)("XXXX")` `(1+tan(pi/4))/(1+cot(pi/4))`

`color(white)("XXXX")` `color(white)("XXXX")` `=(1+1)/(1+1)`

`color(white)("XXXX")` `color(white)("XXXX")` `= 1`

`color(white)("XXXX")` `color(white)("XXXX")` `!= 2`

In fact with very little manipulation it is easy to show:
`color(white)("XXXX")` `(1+tan(x))/(1+cot(x)) = tan(x)`