Question

in triangle ABC cot A + cot B + cot C = √3 . prove that ABC is equilateral in nature.

Answer 1

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