Trignometric manipulation problem

[Dumbledore211]

Homework Statement

If A+B+C=pi where pi=180 and cotA+cotB+cotC=√3 show that A=B=C

Homework Equations

cot(A+B)= cotAcotB-1/cotA+cotB

The Attempt at a Solution

I have tried to solve it by using both A+B+C=pi and cotA+cotB+cotC=√3. I also know that we have manipulate the whole expression in such a way that the end result that we get is cotA=cotB=cotC. What confuses is how we can use cotA+cotB+cotC=√3 effectively

 

[haruspex]

Often a way to show something like x=y and u=v is to show that (x-y)²+(u-v)²=0.
Another hint is to consider cot(A+B+C).

 

[Dumbledore211]

Initially, I have tried to solve it by considering cot(A+B+C). But, my real question to you guys is how do I eliminate √3 from the expression √3= cotAcotBcotC-1 where cotA+cotB+cotC=√3.

 

[Dumbledore211]

Since there is a √3 the expression should look something like cot^3A+ cot^3B+cot^3C-3cotAcotBcotC=0 so that we can get the final result 1/2(cotA+cotB+cotC){(cotA-cotB)^2+(cotB-cotC)^2+(cotC-cotA)^2}=0. What is baffling me is How do I get there by using cot(A+B+C) and A+B+C=pi where pi=180

 

[HallsofIvy]

Please do not use standard math symbols with non-standard meanings! pi= $\pi$= 3.1415926... not "180".

(Yes, $\pi$ radians, angle measure, is equivalent to 180 degrees but that has nothing to do with this problem.)

 

[Dumbledore211]

I am sorry for my mistake. Your help would be very much appreciated if you could give a proper reply to my earlier posts regarding this problem

 

[haruspex]

Initially, I have tried to solve it by considering cot(A+B+C). But, my real question to you guys is how do I eliminate √3 from the expression √3= cotAcotBcotC-1.

I don't know how you reached that expression.
What did you get for cot(A+B+C)? What did setting that equal to cot(pi) tell you about cot A, cot B, cot C?
Did you understand what to do with my other hint?