Question

Please simplify `arctan(x+2)-arctanx` ? Thanks

Answer 1

`arc tan{2/(x+1)^2}`.

Explanation:

We know that, `arctanx-arctany=arctan{(x-y)/(1+xy)}; x,y in RR^+`.

`:. arctan(x+2)-arctanx=arctan{((x+2)-x)/(1+(x+2)x)}`,

`=arctan{2/(x^2+2x+1)}`,

`=arctan{2/(x+1)^2}`.