三角型ABC中,内角A,B,C的对边分别为a,b,c,已知a,b,c,成等比数列,cosB=3/4(1)求1/tanA+1/tanB的值(2)设向量BA点乘向量BC=3/2,求a+c的值
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![三角型ABC中,内角A,B,C的对边分别为a,b,c,已知a,b,c,成等比数列,cosB=3/4(1)求1/tanA+1/tanB的值(2)设向量BA点乘向量BC=3/2,求a+c的值](/uploads/image/z/11472207-15-7.jpg?t=%E4%B8%89%E8%A7%92%E5%9E%8BABC%E4%B8%AD%2C%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%2C%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2CcosB%EF%BC%9D3%2F4%EF%BC%881%EF%BC%89%E6%B1%821%2FtanA%2B1%2FtanB%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%AE%BE%E5%90%91%E9%87%8FBA%E7%82%B9%E4%B9%98%E5%90%91%E9%87%8FBC%EF%BC%9D3%2F2%2C%E6%B1%82a%EF%BC%8Bc%E7%9A%84%E5%80%BC)
三角型ABC中,内角A,B,C的对边分别为a,b,c,已知a,b,c,成等比数列,cosB=3/4(1)求1/tanA+1/tanB的值(2)设向量BA点乘向量BC=3/2,求a+c的值
三角型ABC中,内角A,B,C的对边分别为a,b,c,已知a,b,c,成等比数列,cosB=3/4
(1)求1/tanA+1/tanB的值
(2)设向量BA点乘向量BC=3/2,求a+c的值
三角型ABC中,内角A,B,C的对边分别为a,b,c,已知a,b,c,成等比数列,cosB=3/4(1)求1/tanA+1/tanB的值(2)设向量BA点乘向量BC=3/2,求a+c的值
1.
a,b,c成等比数列,ac=b^2,sinA*sinC=sinB^2 (a/sinA=Bb/sinB=c/sinC=2R)
cotA+cotC= cosA /sinA +cosC /sinC
=(cosA sinC +cosC sinA )/sinA sinC
=sin(A+C )/sinB ^2
=sinB /sin B^2
=1/sinB
=根号(1-cosB^2)=根号7/4
2.
a、b、c成等比数列,b^2=ac
(向量BA)*(向量BC)=|BA|*|BC|cosB=ac*0.75=1.5,
ac=2
由余弦定理:
b^2=a^2+c^2-2accosB
ac=a^2+c^2-1.5ac
a^2+c^2=2.5ac=5
(a+c)^2=a^2+c^2+2ac=9
故a+c=3
a,b,c成等比数列,ac=b^2,sinA*sinC=sinB^2 (a/sinA=Bb/sinB=c/sinC=2R)
cotA+cotC= cosA /sinA +cosC /sinC
=(cosA sinC +cosC sinA )/sinA sinC
=sin(A+C )/sinB ^2
=sinB /sin B^2
=1/sinB
=根号(1-cosB^2)=根号7/4