高中函数难题急需解答

高中三角函数问题。急！谢谢！！在

1)1+tanA/tanB=2c/b --->1+(sinA/cosA)/(sinB/cosB)=2(2RsinC)/(2RsinB) --->1+(sinAcosB)/(cosAsinB)=2sinC/sinB --->(sinAcosB+cosAsinB)/(cosAsinB)=2sinC/sinB --->sin(A+B)/(cosAsinB)=2sin(A+B)/sinB △ABC中sin(A+B)=sinC<>0,sinB<>0 --->2cosA=1 --->cosA=1/2 --->A=60° 2)m+n=(cosB,-1+2[cos(C/2)]^2)=(cosB,cosC)...全部

  1)1+tanA/tanB=2c/b --->1+(sinA/cosA)/(sinB/cosB)=2(2RsinC)/(2RsinB) --->1+(sinAcosB)/(cosAsinB)=2sinC/sinB --->(sinAcosB+cosAsinB)/(cosAsinB)=2sinC/sinB --->sin(A+B)/(cosAsinB)=2sin(A+B)/sinB △ABC中sin(A+B)=sinC<>0,sinB<>0 --->2cosA=1 --->cosA=1/2 --->A=60° 2)m+n=(cosB,-1+2[cos(C/2)]^2)=(cosB,cosC) |m+n|=√[(cosB)^2+(cosC)^2] =√[(1+cos2B)/2+(1+cos2C)/2] =√[1+(cos2B+cos2C)/2] =√[1+cos(B+C)cos(B-C)] 【和差化积】 =√[1-cosAcos(B-C)] =√[1-(1/2)cos(B-C)] 当仅当B=C时cos(B-C)取得最大值1 --->1-cos(B-C)>=1-1=0 所以|m+n|有最小值0。
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