三角函数:已知角A、B、C是△ABC的内角,向量m=(1,根号3),n=(sin(π-A),sin(A-π/2)),m垂

1
m垂直于n
向量m垂*n=0
∴(1,根号3)*(sin(180-A),sin(A-90))=0
∵sin(180-A)=sinA,sin(A-90)=-cosA
∴(1,√3)*(sinA,-cosA)=0
==>sinA-√3cosA=0
==>tanA=√3
∵A 是三角形ABC的内角
∴A=π/3
2
y=2sin²B+cos(60-2B)
=1-cos2B+1/2cos2B+√3/2 sin2B
=1+√3/2 sin2B-1/2cos2B
=1+sin(2B-π/6)
∵B=π-A-C=2π/3-C
∴B∈(0,2π/3)
-π/6