设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?
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![设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?](/uploads/image/z/6990138-18-8.jpg?t=%E8%AE%BE%E9%94%90%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%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.a%3D2bsinA.%E6%B1%82cosA%EF%BC%8BsinC%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%3F%E8%AE%BE%E9%94%90%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%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.a%3D2bsinA.%E6%B1%82cosA%EF%BC%8BsinC%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%3F)
设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?
设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?
设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?
设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?设锐角三角形ABC的内角A,B,C的对边分别为a,b,c.a=2bsinA.求cosA+sinC的取值范围?
因为a=2bsinA ,所以a/sinA=b/sinB=2b 所以sinB=1/2,所以B=π/6 A+C=5π/6,C=5π/6-C cosA+cosC=cosA+cos(5π/6-A)=cosA+1/2cosA+√3/2sinA =3/2cosA+√3/2sinA=√3sin(A+π/3) 因为为锐角三角形,所以π/3<A<π/2 A+π/3∈(2π/3,5π/6) sin(A+π/3)∈(1/2,√3/2) 所以cosA+sinC∈(√3/2,3/2)