已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)...已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)求Bo的大小(2)当B=(3Bo)/4时,求cosA-cosC的值.
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![已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)...已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)求Bo的大小(2)当B=(3Bo)/4时,求cosA-cosC的值.](/uploads/image/z/8704210-58-0.jpg?t=%E5%B7%B2%E7%9F%A5A%E3%80%81B%E3%80%81C%E6%98%AF%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%2C%E4%B8%94%E6%BB%A1%E8%B6%B32sinB%3DsinA%2BsinC%2C%E8%AE%BEB%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BABo.%281%29...%E5%B7%B2%E7%9F%A5A%E3%80%81B%E3%80%81C%E6%98%AF%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%2C%E4%B8%94%E6%BB%A1%E8%B6%B32sinB%3DsinA%2BsinC%2C%E8%AE%BEB%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BABo.%281%29%E6%B1%82Bo%E7%9A%84%E5%A4%A7%E5%B0%8F%282%29%E5%BD%93B%3D%283Bo%29%2F4%E6%97%B6%2C%E6%B1%82cosA-cosC%E7%9A%84%E5%80%BC.)
已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)...已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)求Bo的大小(2)当B=(3Bo)/4时,求cosA-cosC的值.
已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)...
已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)求Bo的大小(2)当B=(3Bo)/4时,求cosA-cosC的值.
已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)...已知A、B、C是三角形ABC的三个内角,且满足2sinB=sinA+sinC,设B的最大值为Bo.(1)求Bo的大小(2)当B=(3Bo)/4时,求cosA-cosC的值.
1、∵2sinB=sinA+sinC=2sin[(A+C)/2]cos[(A-C)/2]
=2sin[(π-B)/2]cos[(A-C)/2]=2cos(B/2)cos[(A-C)/2]
∴4sin(B/2)cos(B/2)=2cos(B/2)cos[(A-C)/2]
∴sin(B/2)=(1/2)cos[(A-C)/2]≤1/2
∴B/2≤π/6
∴B≤π/3
∴B0=π/3
2、B=3B0/4=π/4
则2sinB=sinA+sinC=√2……………………①
设cosA-cosC=x……………………②
①²+②²得
(sinA+sinC)²+(cosA-cosC)=2+x²
sin²A+sin²C+2sinAsinC+cos²A+cos²C-2cosAcosC=2+x²
2-2(cosAcosC-sinAsinC)=2+x²
2-2cos(A+C)=2+x²
所以x²=-2cos(A+C)=2cosB=√2
所以cosA-cosC=x=±(2的4次方根)