Question

已知A B C为锐角三角形的三个内角 向量m=(2-2sinA,cosA+sinA)与n=(sinA-cosA,1+si

Answer 1

1

A=π/3

2

B+C=2π/3,故：C-3B=2π/3-4B

y=2sinB^2+cos((C-3B)/2)

=1-cos(2B)+cos(π/3-2B)

=1-cos(2B)+cos(2B)/2+√3sin(2B)/2

=1-cos(2B)/2+√3sin(2B)/2

=sin(2B-π/6)+1

B∈(0,2π/3),即：2B-π/6∈(-π/6,7π/6)

故：sin(2B-π/6)∈(-1/2,1]

即：y∈(1/2,2]