Question

已知向量a=(sinA,cosA),b=(cosC,sinC),若根号3的a乘以b=sin2B ,且A,B,C为△ABC

Answer 1

√3(a.b)=√3(sinA,cosA).(cosC,sinC)

√3(sinAcosC+cosAsinC)=sin2B

√3sin(A+C)=2sinBcosB

√3sinB=2sinBcosB

在△ABC中sinB≠0

则：√3=2cosB

即：cosB=√3/2

所以：∠B=π/6