Approximate formula

[Yegor]

There exist such a formula for large x:
\arctan(x)\approx \pi/2-1/x+1/3x^3...
I can't understand how it is derived. I tried to get it from Taylor series (for x -> infinity) and understood that here is something different. Can someone help me?
Thank you

[qbert]

have you tried arctan(1/x) for x->0?

and note:
arctan(1/x) = Pi/2 - arctan(x)

[Yegor]

Hm. This is what i got:
f(x)=\arctan(1/x);
f'(x)=-\frac{1}{1+x^2};
f(x)\approx f(0)+f'(0)(x-0)=\pi/2-x
yes. it looks good

[Yegor]

Great. i got next terms too. Thank you very much.