Question

arctan1/2+arctan1/5+arctan1/3

Answer 1

tana1=1/5,tana2=1/3 tana3=1/2 上式=a1+a2+a3

tan(a1+a2)=(tana1+tana2)/(1-tana1tana2)=4/7 a1+a2=arctan4/7 tan(a1+a2+a3)=[tan(a1+a2)+tana3]/(1-tan(a1+a2)tana3) =3/2 所以a1+a2+a3 =arctan(3/2)