已知A,B为锐角,向量a=(cos∠ A,sin ∠A),b=(cosB ,sinB).c=(1/2,1/2).若a*b

a*b=cosAcosB+sinBsinA =cos(A-B)=(√2)/2 =>|B-A|=π/4 =>2B-2A=π/2或者-π/2.
a*c=(√3-1)/4=1/2cosA+1/2sinA =√2/2cos(π/4-A)=(√3-1)/4 =>|π/4-A|=π/12 =>A=π/6或者π/3.
2B-A=2B-2A+A有四中可能.
=π/2+π/6=2π/3 (1)
=π/2+π/3=5π/6 (2)
=-π/2+π/6=-π/3 (3)
=-π/2+π/3=-π/6 (1)

向量a乘以向量b=cosAcosB+sinBsinA
=cos(A-B)=(√2)/2
可得,cos(2A-2B).
向量a乘以向量c=1/2cosA-1/2sinA
=1/2sin(45-A)=（√3-1）/4
得sin(45-A)=（√3-1）/2
又可得,cos(90-A)=1-2sin(45-A)^2=
可得出sinA,
所以,sin(2B-A)就出来了