（1）∵(m+n)(m-n)=sinBsinC
∴ m²-n²=sinBsinC
即 (sinB+sinC)²-sin²A=sinBsinC
∴ sin²B+sin²C-sin²A=-sinBsinC
由 正弦定理 a/sinA=b/sinB=c/sinC 和
余弦定理 cosA=(b²+c²-a²)/2bc 得
cosA=(sin²B+sin²C-sin²A)/2sinBsinC
∴ cosA=-sinBsinC/2sinBsinC=-1/2
又 角A为△ABC的内角
∴ A=2π/3
（2）由（1）,可知
B+C=π/3
则 B=π/3-C
∴ sinB+sinC=sin(π/3-C)+sinC
=sinπ/3cosC-cosπ/3sinC+sinC
=sinπ/3cosC+cosπ/3sinC
=sin(C+π/3)
又 C∈(0,π/3)
∴ (C+π/3)∈(π/3,2π/3)
∴ sin(C+π/3)∈(√3/2,1]
∴ sinB+sinC∈(√3/2,1]
因此 sinB+sinC的取值范围为(√3/2,1]