Question

已知函数y=arctanx+arctan(1-x/1+x)求值域

Answer 1

y=arctanx+arctan(1-x/1+x)

tany=tan[arctanx+arctan(1-x/1+x)]=[x+(1-x)/(1+x)]/[1-x*(1-x)/(1+x)]=1

∴y=kπ+π/4