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

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Question 96996: If cotA + cotB + cotC=sqrt3 then prove that the triangle is equilateral.
Answer by mathslover(135) About Me  (Show Source):
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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