Question

若2*sinA=1+cosA,A不等于kπ（k属于Z)则tan(A/2)为

Answer 1

由2*sinA=1+cosA,有:

4sin(A/2)cos(A/2)=1+[cos(A/2)]^2-[sin(A/2)]^2

即:4sin(A/2)cos(A/2)=2[cos(A/2)]^2

所以:cos(A/2)*[2sin(A/2)-cos(A/2)]=0

因为A不等于kπ

所以cos(A/2)≠0

所以2sin(A/2)-cos(A/2)=0

2sin(A/2)=cos(A/2)

tan(A/2)=sin(A/2)÷cos(A/2)=1/2