Question

How do you prove the identity `tan2XcotX=3`?

Answer 1

It isn't.

Explanation:

`tan(2x)*cot(x) = 3`

Using the double angle formula,

`(2tan(x))/(1-tan^2(x))*cot(x) = 3`

Knowing that `tan(x)*cot(x) = 1`

`2/(1-tan^2(x)) = 3`

Which is obviously false, as the tangent range from `-oo` to `oo`.
If you continue to work this like it was an equation, you'll see this only has two tangent values for solutions, `+-sqrt(3)/3`.