设△ABC是锐角三角形a.b.c分别是内角A.B.C所对边长,并且sin^A=sin(π/3+B)sin(π/3-B)+sin^B.1.求角A的2.若向量AB*向量AC=12,a=2√7,求b,c(其中b<c)
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![设△ABC是锐角三角形a.b.c分别是内角A.B.C所对边长,并且sin^A=sin(π/3+B)sin(π/3-B)+sin^B.1.求角A的2.若向量AB*向量AC=12,a=2√7,求b,c(其中b<c)](/uploads/image/z/1946428-52-8.jpg?t=%E8%AE%BE%E2%96%B3ABC%E6%98%AF%E9%94%90%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2a.b.c%E5%88%86%E5%88%AB%E6%98%AF%E5%86%85%E8%A7%92A.B.C%E6%89%80%E5%AF%B9%E8%BE%B9%E9%95%BF%2C%E5%B9%B6%E4%B8%94sin%5EA%3Dsin%28%CF%80%2F3%2BB%29sin%28%CF%80%2F3-B%29%2Bsin%5EB.1.%E6%B1%82%E8%A7%92A%E7%9A%842.%E8%8B%A5%E5%90%91%E9%87%8FAB%2A%E5%90%91%E9%87%8FAC%3D12%2Ca%3D2%E2%88%9A7%2C%E6%B1%82b%EF%BC%8Cc%EF%BC%88%E5%85%B6%E4%B8%ADb%EF%BC%9Cc%EF%BC%89)
设△ABC是锐角三角形a.b.c分别是内角A.B.C所对边长,并且sin^A=sin(π/3+B)sin(π/3-B)+sin^B.1.求角A的2.若向量AB*向量AC=12,a=2√7,求b,c(其中b<c)
设△ABC是锐角三角形a.b.c分别是内角A.B.C所对边长,并且sin^A=sin(π/3+B)sin(π/3-B)+sin^B.1.求角A的
2.若向量AB*向量AC=12,a=2√7,求b,c(其中b<c)
设△ABC是锐角三角形a.b.c分别是内角A.B.C所对边长,并且sin^A=sin(π/3+B)sin(π/3-B)+sin^B.1.求角A的2.若向量AB*向量AC=12,a=2√7,求b,c(其中b<c)
sin^2A=sin(60+B)sin(60-B)+sin^2B
sin^2A=-1/2(cos(60+B+60-B)-cos(60+B-60+B)+sin^2B
sin^2A=-1/2(-1/2-cos2B)+1/2(1-cos2B)
1/2(1-cos2A)=-1/2(-1/2-cos2B)+1/2(1-cos2B)
1-cos2A=1/2+cos2B+1-cos2B
cos2A=-1/2
2A=120度
A=60度
若向量 AB.AC=12,那么cb=24
又a^2=28=b^2+c^2-2bccosA=b^2+c^2-24
所以b^2+c^2=52,结合bc=24,b