化简arctan((1-x)/(1+x))答案是arctan1-arctanx=π/4-arctanx

Question

化简arctan((1-x)/(1+x))
答案是arctan1-arctanx=π/4-arctanx

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