# SOLUTION: If cotA + cotB + cotC=sqrt3 then prove that the triangle is equilateral.

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 Click here to see ALL problems on Triangles Question 96996: If cotA + cotB + cotC=sqrt3 then prove that the triangle is equilateral.Answer by mathslover(135)   (Show Source): You can put this solution on YOUR website!given cotA + cotB + cotC = sqrt3 to prove triangle ABC is equilateral we prove this by assuming ABC to be equialteral and establishing the truth of the statement cotA + cotB + cotC =sqrt3 since ABC is equialteral angleA=angleB=angleC=60 degrees cotA=cotB=CotC = cot60= 1/sqrt3 therefore cotA + cotB + cotC = 1/sqrt3 + 1/sqrt3 + 1/sqrt3 =3/sqrt3 =sqrt3 which is equal to the RHS ( right hand side) of the expression hence our assumption that ABC is equilateral is true