在三角形ABC中,AB=c,BC=a,AC=b,则(sin(A/2))^2+(sin(B/2))^2+(sin(C/2))^2=(cos(B/2))^2成立的充要条件是A.a+b=2cB.b+c=2aC.a+c=2bD.ac=b^2有没有巧法?王霆峰的方法可行,但是需要十分钟以上,一般小题是有简单解法
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![在三角形ABC中,AB=c,BC=a,AC=b,则(sin(A/2))^2+(sin(B/2))^2+(sin(C/2))^2=(cos(B/2))^2成立的充要条件是A.a+b=2cB.b+c=2aC.a+c=2bD.ac=b^2有没有巧法?王霆峰的方法可行,但是需要十分钟以上,一般小题是有简单解法](/uploads/image/z/6950182-22-2.jpg?t=%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CAB%3Dc%2CBC%3Da%2CAC%3Db%2C%E5%88%99%28sin%28A%2F2%29%29%5E2%2B%28sin%28B%2F2%29%29%5E2%2B%28sin%28C%2F2%29%29%5E2%3D%28cos%28B%2F2%29%29%5E2%E6%88%90%E7%AB%8B%E7%9A%84%E5%85%85%E8%A6%81%E6%9D%A1%E4%BB%B6%E6%98%AFA.a%2Bb%3D2cB.b%2Bc%3D2aC.a%2Bc%3D2bD.ac%3Db%5E2%E6%9C%89%E6%B2%A1%E6%9C%89%E5%B7%A7%E6%B3%95%EF%BC%9F%E7%8E%8B%E9%9C%86%E5%B3%B0%E7%9A%84%E6%96%B9%E6%B3%95%E5%8F%AF%E8%A1%8C%EF%BC%8C%E4%BD%86%E6%98%AF%E9%9C%80%E8%A6%81%E5%8D%81%E5%88%86%E9%92%9F%E4%BB%A5%E4%B8%8A%EF%BC%8C%E4%B8%80%E8%88%AC%E5%B0%8F%E9%A2%98%E6%98%AF%E6%9C%89%E7%AE%80%E5%8D%95%E8%A7%A3%E6%B3%95)
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