已知实数a.b均不为零,asinA+bcosA/acosA-bsinA=tanB,B-A=π/6,则b/a=

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已知实数a.b均不为零,asinA+bcosA/acosA-bsinA=tanB,B-A=π/6,则b/a=
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已知实数a.b均不为零,asinA+bcosA/acosA-bsinA=tanB,B-A=π/6,则b/a=
已知实数a.b均不为零,asinA+bcosA/acosA-bsinA=tanB,B-A=π/6,则b/a=

已知实数a.b均不为零,asinA+bcosA/acosA-bsinA=tanB,B-A=π/6,则b/a=
已知实数a.b均不为零,(asinA+bcosA)/(acosA-bsinA)=tanB,B-A=π/6,则b/a=
cosφ=a/√(a²+b²)
sinφ=b/√(a²+b²)
tanφ=b/a
asinA+bcosA=cosφsinA+sinφcosA=sin(A+φ)
acosA-bsinA=cosφcosA-sinφsinA=cos(A+φ)
(asinA+bcosA)/(acosA-bsinA)=tan(A+φ)=tanB
A+φ=B+nπ
φ=B-A+nπ=nπ+π/6
b/a=tanφ=tan(nπ+π/6)=√3/3