Prove that a triangle `A B C` is equilateral if and only if `tanA+tanB+tanC=3sqrt(3)dot`

Prove that a triangle ABC is equilateral if and only if tanA+tanB+tanC=3sqrt(3).

Prove that a triangle ABC is equilateral if and only if tan A+tan B+tan C=3sqrt(3).

Prove that the triangle ABC is equilateral if cot A+cot B+cot C=sqrt(3)

tanA +tanB + tanC = tanA tanB tanC if

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=adot TO PROVE : a r( A B C)=(sqrt(3))/4a^2 CONSTRUCTION : Draw A D_|_B Cdot

In an acute-angled triangle ABC, tanA+tanB+tanC

Statement-1: In an acute angled triangle minimum value of tan alpha + tanbeta + tan gamma is 3sqrt(3) . And Statement-2: If a,b,c are three positive real numbers then (a+b+c)/3 ge sqrt(abc) into in a triangleABC , tanA+ tanB + tanC= tanA. tanB.tanC

In a triangle ABC tanA+tanB+tanC>=P then P=