在斜三角形ABC中tanC/tanA+tanC/tanB=1,则(a^2+b^2)/c^2

summershen001 1年前 已收到1个回答 举报

trl1973 幼苗

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tanC/tanA+tanC/tanB=1
tanBtanC+tanAtanC=tanAtanB
tanC(tanA+tanB)=tanAtanB
sinC/cosC (sinA/cosA+sinB/cosB)=sinAsinB/cosAcosB
sinC (sinAcosB+cosAsinB)=sinAsinBcosC
sinC sin(A+B)=sinAsinBcosC
sinC sin(180°-C)=sinAsinBcosC
sin^2C=sinAsinBcosC
sinC/sinA * sinC/sinB = cosC
c/a * c/b = (a^2+b^2-c^2)/(2ab)
2c^2 = a^2+b^2-c^2
a^2+b^2 = 3c^2
(a^2+b^2)/c^2 = 3

1年前

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