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Saturday, 5 April 2008
Equilateral Triangle
How can you prove that a triangle is equilateral if and only if tan A + tan B + tan C = 3√3 ?
Hint: Related to a chapter in Module - 3 (Mathematics).
ReplyDeleteIf the given triangle is equilateral
ReplyDeleteA=B=C=60, or tan A + tan B + tan C = 3 root 3.
On the other hand, if
tan A + tan B + tan C = 3 root 3.
As A+B+C=180,
tan A . tan B . tan C = 3 root 3.
A.M. = G.M. = root 3.
Thus, tan A = tan B = tan C or A=B=C=60
Hence proved both ways, or proved that a triangle is equilateral iff (if and only if) tan A + tan B + tan C = 3 root 3.