Question

化简arctan((1-x)/(1+x))

Answer 1

公式：

tan(x+y)=(tanx+tany)/(1-tanxtany),tan(π/4)=1,tan(arctanx)=x.

(1-tanx)/(1+tanx)=(tanπ/4-tanx/)(1+tanπ/4tanx)=tan(π/4-x)

(1-x)/(1+x)=(tanπ/4-arctanx)(1+tanπ/4arctanx)=tan(π/4-arctanx)

arctan[(1-x)/(1+x)]=arctan[tan(π/4-arctanx)]=π/4-arctanx