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
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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=√2/2,a*c=(√3-1)/4.求角2B-A
![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](/uploads/image/z/16983314-26-4.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%E4%B8%BA%E9%94%90%E8%A7%92%2C%E5%90%91%E9%87%8Fa%3D%28cos%E2%88%A0+A%2Csin+%E2%88%A0A%29%2Cb%3D%28cosB+%2CsinB%29.c%3D%281%2F2%2C1%2F2%29.%E8%8B%A5a%2Ab)
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)
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)
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