Question

if a/cosA=b/cosB=c/cosC then show that triangle isequilateral

Answer 1

2 answers · Mathematics   Best Answer a/sinA = b/sinB = c/sinC is true for all triangles (the Sine Rule).  If in addition for this particular triangle a/cosA = b/cosB = c/cosC, then by division we must have  tanA = tanB = tanC.  Since each of A, B, C must be between 0 and 180 degrees, and tan(x) has unique values in this range, then  A = B = C.  But A+B+C=180 degrees. So A = B = C = 60 degrees. The triangle is equiangular and therefore also equilateral.

Answer 2

sides are equal........