a/sinA=b/sinB=k
sinA=ak
sinB=bk
2sinB×cosC=sinA
2bkcosC=ak
2bcosC=a
cosC=a/2b
∵cosC=(a^2+b^2-c^2)/2ab=a/2b
∴a^2+b^2-c^2=a^2
∴b^2=c^2
∴b=c
∴∠B=∠C

(2)
cosA=(b^2+c^2-a^2)/2bc
=(2b^2-1)/2b^2=-1/2
2b^2-1=-b^2
b=c=√3/3
S△ABC=1/2*bcsinA
=1/2*√3/3*√3/3*√3/2
=√3/12
希望对你能有所帮助.