menalide
春芽
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acosC+√3 asinC-b-c=0
acosC+√3 asinC=b+c
由正弦定理,得
sinAcosC+√3 sinAsinC
=sinB+sinC
=sin(A+C)+sinC
=sinAcosC+sinCcosA+sinC
即,√3 sinAsinC =sinCcosA+sinC
因为sinC≠0
所以,√3 sinA-cosA=1
sin(A-30°)=1/2
A=60°
1年前
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tjadeng
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sinAcosC+√3 sinAsinC =sinB+sinC =sin(A+C)+sinC 这里是什么意思!
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menalide
acosC+√3 asinC=b+c a(cosC+√3 sinC)=b+c 由正弦定理,得 a/sinA=c/sinC=b/sinB a=csinA/sinC sinB=bsinC/c csinA/sinC(cosC+√3 asinC)=b+c sinA(cosC+√3 asinC)=(b+c)*sinC/c sinAcosC+√3 sinAsinC=bsinC/c +sinC sinAcosC+√3 sinAsinC=sinB+sinC sinAcosC+√3 sinAsinC=sin(180-(A+C))+sinC sinAcosC+√3 sinAsinC=sin(A+C)+sinC