Question

arctan1-arctan[x/(x+1)]=arctan[1/(2x+1)],怎么算出来的?

Answer 1

是还原成正切计算的.arctan1=π/4,设arctan[x/(x+1)]=α,则　tanα=x/(x+1)　,α∈(-π/2,π/2)tan(π/4-α)=(1-tanα)/(1+tanα)=[1-x/(x+1)]/[1+x/(x+1)]=1/(2x+1)所以　π/4-α＝arctan[1/(2x+1)],即arctan1-arct...