1)因为向量 n 与x轴正向同向,因此向量 m 与x轴正向夹角为 π/3 ,
所以由 1-cosB>0 得 tan(π/3)=(1-cosB)/sinB ,
化简得 1-cosB=√3sinB ,
√3sinB+cosB=1 ,
√3/2*sinB+1/2*cosB=1/2 ,
sin(B+π/6)=1/2 ,
因此 B+π/6=π/6 或 B+π/6=5π/6 ,
解得 B=2π/3 (舍去0).
2)b=√3,
根据正弦定理可得:b/sinB=a/sinA=c/sinC,
而b/sinB=√3/sin2π/3=2,
所以a= 2sinA,c=2 sinC.
a+c= 2(sinA +sinC).
因为 A+C=π-B=π/3 ,
所以 sinA+sinC=sinA+sin(π/3-A)
=sinA+sin(π/3)cosA-cos(π/3)sinA
=sinA+√3/2*cosA-1/2*sinA
=1/2*sinA+√3/2*cosA
=sin(A+π/3)
由于 0