SOLUTION: In ΔABC, Given (a/cosA)=(b/cosB)=(c/cosC) . Prove that ΔABC is an equilateral triangle.

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Question 252352: In ΔABC, Given (a/cosA)=(b/cosB)=(c/cosC) . Prove that ΔABC is an equilateral triangle.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
In ΔABC, Given (a/cosA)=(b/cosB)=(c/cosC) . Prove that ΔABC is an equilateral triangle. 


By the law of sines:



and therefore



Multiplying equals by equals:









A,B, and C are angles of a triangle and thus are less than 180°.

Any two angles less than 180° which have the same tangent must
be equal in measure.  Thus

A = B = C

Thus triangle ABC is equiangular and every equiangular
triangle is also equilateral.

Edwin
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