Question

在△ABC中,A,B,C是三角形的内角,a,b,c是三内角对应的三边,已知a=2√3,c=2,(sinAcosB)/(sinBcosA)=(2c-b)/b

求∠A

Answer 1

sinAcosB/sinBcosA=2c-b/b
用b=2RsinB，c=2RsinC代入

sinAcosB/sinBcosA=2sinC-sinB/sinB
sinAcosB/cosA=2sinC-sinB
sinAcosB=2sinCcosA-sinBcosA
sinAcosB+sinBcosA=2sinCcosA
sin(A+B)=2sinCcosA
sinC=2sinCcosA
1=2cosA
cosA=1/2

A,B,C为三角形内角，所以∠A=60°