已知abc分别是△ABC中角ABC的对边,若abc成等比数列,求证(1/tanA)+(1/tanC)=(1/sinB)
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已知abc分别是△ABC中角ABC的对边,若abc成等比数列,求证(1/tanA)+(1/tanC)=(1/sinB)
已知abc分别是△ABC中角ABC的对边,若abc成等比数列,求证(1/tanA)+(1/tanC)=(1/sinB)
已知abc分别是△ABC中角ABC的对边,若abc成等比数列,求证(1/tanA)+(1/tanC)=(1/sinB)
(1/tanA)+(1/tanC)=cosA/sinA+ cosC/sinC=sin(A+C)/(sinAsinC)=sinB/(sinAsinC)
由正弦定理得sinB/(sinAsinC)=b/(ac)
因为abc成等比,故b/(ac)=1/b=1/sinB
所以(1/tanA)+(1/tanC)=(1/sinB)
等比数列:a/b=b/c
由正弦定理:a/b=sinA/sinB,b/c=sinB/sinC
sinA/sinB=sinB/sinC
(sinB)^2=sinAsinC
(1/tanA)+(1/tanC)=cosA/sinA+ cosC/sinC
=(sinAcosC+cosAsinC)/(sinAsin...
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等比数列:a/b=b/c
由正弦定理:a/b=sinA/sinB,b/c=sinB/sinC
sinA/sinB=sinB/sinC
(sinB)^2=sinAsinC
(1/tanA)+(1/tanC)=cosA/sinA+ cosC/sinC
=(sinAcosC+cosAsinC)/(sinAsinC)
=sin(A+C)/(sinB)^2
=sin(180°-B)/(sinB)^2
=sinB/(sinB)^2
=1/sinB
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