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Homework Help: A problem in Trigonometry (Properties of Triangles) v2

  1. May 11, 2017 #1

    Wrichik Basu

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    1. The problem statement, all variables and given/known data

    In any triangle ABC, prove that $$ a^2 + b^2 +c^2 =4 \Delta (\cot {A}+\cot {B}+\cot {C}) $$

    2. Relevant equations

    3. The attempt at a solution

    14945181329111154603192.jpg
     
  2. jcsd
  3. May 11, 2017 #2
    What is ##\Delta## ?
     
  4. May 11, 2017 #3

    Wrichik Basu

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    The area of Triangle, the standard notation used in Trigonometry.
     
  5. May 11, 2017 #4
    ##\displaystyle {c \over \sin c} = 2R##

    Check your work again, you replace ##\sin c## with ##a/(2R)##, you should do ##c/(2R)##
     
  6. May 11, 2017 #5

    Wrichik Basu

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    You are wrong: $$\frac {c} {\sin (c)} = 2R$$ not $$\frac {c}{\sin ^2 (c)} = 2R$$
     
    Last edited by a moderator: May 11, 2017
  7. May 11, 2017 #6
    Yes, that was a typo. o0)o0):-p
     
    Last edited by a moderator: May 11, 2017
  8. May 11, 2017 #7

    Mark44

    Staff: Mentor

    No, this is not standard notation for the area of a triangle. Δ is sometimes used for the discriminant of a quadratic equation, but I have never seen it used for area of any kind.
     
  9. May 12, 2017 #8

    Wrichik Basu

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    Although notations shouldn't very, h ere in India we use Delta to distinguish the area of the triangle only on Trigonometry.

    Discriminant is shown by D.
     
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