Question

How to solve the ecuation Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=(Pi/4) ?

Answer 1

`Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=pi/4`

`=>Arctan(((x-1)/(x-2)+(x+1)/(x+2))/(1-(x^2-1)/(x^2-4)))=pi/4`

`=>(x^2+x-2+x^2-x-2)/(x^2-4-x^2+1)=1`

`=>2x^2-4=-3`

`=>x=pm1/sqrt2`