根据题意
cos(a/2)=2sina
cos(a/2)=4sin(a/2)cos(a/2)
sin(a/2)=1/4
sin²(a/2)+cos²(a/2)=1
解出cos(a/2)=±√15/4
tan(a/2)=sin(a/2)/cos(a/2)=±√15/15