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Skyla Byrd
Mathematics
4 November, 12:23
Prove cotA+cotB+cotC > = square root of 3
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Jayda Mack
4 November, 12:51
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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
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