3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c
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![3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c](/uploads/image/z/1604658-66-8.jpg?t=3+%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2C%E5%B7%B2%E7%9F%A5%EF%BC%88a2%2Bb2%EF%BC%89sin%EF%BC%88A-B%EF%BC%89%3D%EF%BC%88a2-b2%EF%BC%89sin%28A%2BB%29+%E6%B1%82%E8%AF%81%EF%BC%9AABC%E6%98%AF%E7%AD%89%E8%85%B0%E6%88%96%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2%28a%5E2%2Bb%5E2%29sin%28A-B%29%3D%28a%5E2-b%5E2%29sin%28A%2BB%29%2C%28sin%5EA%2Bsin%5EB%29sin%28A-B%29%3D%28sin%5EA-sin%5EB%29sin%28A%2BB%29+sin%5EA%2A%28sin%28A%2BB%29-sin%28A-B%29%29%3Dsin%5EB%2A%28sin%28A-B%29%2Bsin%28A%2BB%29%29+sin%5EA%2A2c)
3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c
3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形
(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),
(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B)
sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B))
sin^A*2cosAsinB=sin^B*2sinAcosB
sin^A*2cosAsinB-sin^B*2sinAcosB=0
sinAsinB(sin2A-sin2B)=0
sin2A=sin2B
2A=2B 或2A+2B=180度
A=B或A+B=90度
故△ABC是等腰三角形或直角三角形
其中,sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) ,也就是第三步怎么来的
3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c
他这是合并同类项
(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B)
sin^Asin(A-B)+ sin^Bsin(A-B)=sin^Asin(A+B) -sin^Bsin(A+B)
sin^A*sin(A+B)-sin^Asin(A-B))=sin^B*sin(A-B)+sin^Bsin(A+B)
sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B))