Question

△ABC中,a,b,c,分别为内角A,B,C的对边,且2asinA=(2b+c)sinB+(2c+b)sinC

Answer 1

：∵sinA/a=sinB/b=sinC/c=1/2R

∴2a^2=(2b+c)b+(2c+b)c

=2b^2+2c^2+2bc

∴b^2+c^2-a^2=-bc

即cosA=(b^2+c^2-a^2)/2bc=-1/2

A=120°

∴B＋C＝60°

sinB+sinC=sinB+sin(60-B)

=sinB+√3/2*cosB-1/2*sinB

=√3/2*cosB+1/2*sinB

=sin(B+60)

当B=30°时,sinB+sinC最大取1