SOLUTION: 1. In a Triangle ABC, if cotA+cotB+cotC=√3 then prove that the triangle is equilateral triangle.

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Question 1017353: 1. In a Triangle ABC, if cotA+cotB+cotC=√3 then prove that the triangle is equilateral triangle.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We use the identity that if A, B, C are angles of a triangle, then

Dividing both sides by , we obtain

(1)

The left-hand side equals , so after some rearranging we get:



Using the fact that :

(2)

(2)*2 + (1)*-2 yields the nice expression:



which implies that or . Therefore, .