新聞雲

標題:

amaths

發問:

• 巨商的李信神2轉點升點--@1@
• 一部平.靚.正的notebook-
• 恆等式與因式分解@1@

此文章來自奇摩知識+如有不便請留言告知

In triangle ABC , a/cosA = b/cosB = c/cosC . What kind of triangle is triangle ABC ?

最佳解答:

By Sine rule, a/sinA=b/sinB=b/sinC=k a = k sin A Therefore, a/cosA = k sinA/ cos A = k tan A Similarly, b/cosB = k tan B and c/cosC = k tan C So, k tan A = k tan B = k tan C i.e., tan A = tan B = tan C Since 0
其他解答:

Let a/cosA = m a/m = cosA b/m = cos B c/m = cos C By cosine rule: a^2 = b^2 + c^2 - 2bc cos A = b ^2 + c^2 - 2bc (a/m) a^2 = b^2 + c^2 - 2abc/m ---(1) b^2 = a^2 + c^2 - 2abc/m --- (2) c^2 = b^2 + a^2 - 2abc/m --- (3) (1) - (2) : a^2 - b^2 = b^2 - a^2 2a^2 = 2b^2 a = b Similarly b=c