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Trignometric manipulation problem

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data
    If A+B+C=pi where pi=180 and cotA+cotB+cotC=√3 show that A=B=C


    2. Relevant equations
    cot(A+B)= cotAcotB-1/cotA+cotB


    3. 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
     
  2. jcsd
  3. Nov 23, 2012 #2

    haruspex

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    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).
     
  4. Nov 23, 2012 #3
    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.
     
  5. Nov 23, 2012 #4
    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
     
    Last edited: Nov 23, 2012
  6. Nov 23, 2012 #5

    HallsofIvy

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    Please do not use standard math symbols with non-standard meanings! pi= [itex]\pi[/itex]= 3.1415926... not "180".

    (Yes, [itex]\pi[/itex] radians, angle measure, is equivalent to 180 degrees but that has nothing to do with this problem.)
     
  7. Nov 23, 2012 #6
    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
     
  8. Nov 23, 2012 #7

    haruspex

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    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?
     
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