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Prove that a triangle A B C is equilater...

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

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We know, in an equilateral triangle,
`/_A = /_B = /_C = 60^@`
`:. tanA+tanB+tanC = tan60^@+tan60^@+tan60^@`
`=sqrt3+sqrt3+sqrt3 = 3sqrt3`
`:. tanA+tanB+tanC = 3sqrt3`
Thus, we can say that a triangle `ABC` is equilateral only if `tanA+tanB+tanC = 3sqrt3.`
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