已知tana/2=2/3,则(1-cosa+sina)/(1+cosa+sina)=
问题描述:
已知tana/2=2/3,则(1-cosa+sina)/(1+cosa+sina)=
答
(1-cosa+sina)/(1+cosa+sina)=(2sin²(a/2)+2sin(a/2)cos(a/2))/(2cos²(a/2)+2sin(a/2)cos(a/2))=sin(a/2)(sin(a/2)+cos(a/2))/(cos(a/2)(sin(a/2)+cos(a/2)))=sin(a/2)/cos(a/2)=tan(a/2) =2/3