Value of arctan (1+sqrt2)-arctan(1-sqrt2) ?

Question

How do u find the value (no calculators or other garbage)

How do u derive it?

Answer 1

The general formula is
arctan(x)-arctan(y)=
arctan[(x-y)/(1+xy)].
In your case, x=1+sqrt(2), y=1-sqrt(2), so
x-y=2sqrt(2) and xy=-1. Thus, you get
arctan(2sqrt(2)/0)=pi/2.

Answer 2

arctan (1+sqrt2)-arctan(1-sqrt2) = arctan (1+sqrt(2) - 1+sqrt(2))/(1+(1+sqrt2)(1-sqrt2)) = arctan(2sqrt2/0) = pi/2