Question

How do you simplify `tan(2 arctan x)`?

Answer 1

tan (2x)

Explanation:

arctanx --> x
tan (2arctan x) --> tan (2x)

Answer 2

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

Explanation:

Let `arctanx=theta`, then

`x=tantheta`

`tan(2arctanx)=tan2theta`

= `(2tantheta)/(1-tan^2theta)`

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