已知A.B.C.是三角形A.B.C的三个内角,向量m=(-2,1),n=(cos(A+π/6),sin(A-π/3)),且m垂直n求角A 若sin²C-cos²C/(1-sin2C)=-2,求tanB的值
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![已知A.B.C.是三角形A.B.C的三个内角,向量m=(-2,1),n=(cos(A+π/6),sin(A-π/3)),且m垂直n求角A 若sin²C-cos²C/(1-sin2C)=-2,求tanB的值](/uploads/image/z/6832147-67-7.jpg?t=%E5%B7%B2%E7%9F%A5A.B.C.%E6%98%AF%E4%B8%89%E8%A7%92%E5%BD%A2A.B.C%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%2C%E5%90%91%E9%87%8Fm%3D%28-2%2C1%29%2Cn%3D%28cos%28A%2B%CF%80%2F6%29%2Csin%28A-%CF%80%2F3%29%29%2C%E4%B8%94m%E5%9E%82%E7%9B%B4n%E6%B1%82%E8%A7%92A+%E8%8B%A5sin%26%23178%3BC-cos%26%23178%3BC%2F%EF%BC%881-sin2C%EF%BC%89%3D-2%2C%E6%B1%82tanB%E7%9A%84%E5%80%BC)
已知A.B.C.是三角形A.B.C的三个内角,向量m=(-2,1),n=(cos(A+π/6),sin(A-π/3)),且m垂直n求角A 若sin²C-cos²C/(1-sin2C)=-2,求tanB的值
已知A.B.C.是三角形A.B.C的三个内角,向量m=(-2,1),n=(cos(A+π/6),sin(A-π/3)),且m垂直n
求角A 若sin²C-cos²C/(1-sin2C)=-2,求tanB的值
已知A.B.C.是三角形A.B.C的三个内角,向量m=(-2,1),n=(cos(A+π/6),sin(A-π/3)),且m垂直n求角A 若sin²C-cos²C/(1-sin2C)=-2,求tanB的值
1
m=(-2,1),n=(cos(A+π/6),sin(A-π/3))
m⊥n,即:m·n=(-2,1)·(cos(A+π/6),sin(A-π/3))
=-2cos(A+π/6)+sin(A-π/3)
=-2(√3cosA/2-sinA/2)+(sinA/2-√3cosA/2)
=3sinA/2-3√3cosA/2
=3sin(A-π/3)=0
即:sin(A-π/3)=0
A∈(0,π),即:A-π/3∈(-π/3,2π/3)
即:A-π/3=0
即:A=π/3
2
(sin²C-cos²C)/(1-sin2C)
=(sinC+cosC)(sinC-cosC)/(sinC-cosC)^2
=(sinC+cosC)/(sinC-cosC)=-2
即:3sinC=cosC
即:tanC=1/3
B+C=2π/3,即:B=2π/3-C
即:tanB=tan(2π/3-C)
=(tan(2π/3)-tanC)/(1+tan(2π/3)tanC)
=(-√3-1/3)/(1-√3/3)
=-(6+5√3)/3
m垂直n。m*n=-2cos(A+π/6)+sin(A-π/3)=-sin(A-π/3)=0,A=π/3
若(sin²C-cos²C)/(1-sin2C)=-2,求tanB的值(cosC+sinC)/(cosC-sinC)=2.
tanC=1/3,tanB=tan[180-(A+C)]=-(tanA+tanC)/(1-tanAtanC)=-(8倍根号3-3)/6
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