document.write( "Question 252352: In ΔABC, Given (a/cosA)=(b/cosB)=(c/cosC) . Prove that ΔABC is an equilateral triangle. \n" ); document.write( "
Algebra.Com's Answer #184276 by Edwin McCravy(20055)\"\" \"About 
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In ΔABC, Given (a/cosA)=(b/cosB)=(c/cosC) . Prove that ΔABC is an equilateral triangle.\r
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document.write( "By the law of sines:\r\n" );
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document.write( "\"a%2F%28sinA%29=b%2F%28sinB%29=c%2F%28sinC%29\"\r\n" );
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document.write( "and therefore\r\n" );
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document.write( "\"%28sinA%29%2Fa=%28sinB%29%2Fb=%28sinC%29%2Fc\"\r\n" );
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document.write( "Multiplying equals by equals:\r\n" );
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document.write( "\"%28%28sinA%29%2F%28cosA%29%29=%28%28sinB%29%2F%28cosB%29%29=%28%28sinC%29%2F%28cosC%29%29\"\r\n" );
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document.write( "\"tanA=tanB=tanC\"\r\n" );
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document.write( "A,B, and C are angles of a triangle and thus are less than 180°.\r\n" );
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document.write( "Any two angles less than 180° which have the same tangent must\r\n" );
document.write( "be equal in measure.  Thus\r\n" );
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document.write( "A = B = C\r\n" );
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document.write( "Thus triangle ABC is equiangular and every equiangular\r\n" );
document.write( "triangle is also equilateral.\r\n" );
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document.write( "Edwin
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