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
