Question

How do you solve `Arc tan(1-x) - arc tanx = pi`?

Answer 1

`x=1/2`

Explanation:

As `arctan(1-x)-arctanx=pi`

`arctan(1-x)=pi+arctanx`

Now taking tangent of both sides

`tan(arctan(1-x))=tan(pi+arctanx)=tan(arctanx)`

or `1-x=x`

or `2x=1` or `x=1/2`