Question

arctanx-arctany可不可以化成arctan() 括号里面是x y的关系式啊 即arctanx-arctany=arctan( )

Answer 1

解:-п/2<arctanx<п/2,
0<arccoty<п. tan(arctanx)=x, tan(arctany)=y. tan(arctanx-atctany) =[tan(arctanx)-tan(arctany)]/[1+tan(arctanx)tan(arctany) =(x-y)/(1+xy).
∴arctanx-arctay=arctan[(x-y)/(1+xy)].

Answer 2

arctanx - arctany =arctan{(x-y)/(1+xy)}