A problem in Trigonometry (Properties of Triangles) v2

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1. May 11, 2017

Wrichik Basu

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

2. May 11, 2017

Buffu

What is $\Delta$ ?

3. May 11, 2017

Wrichik Basu

The area of Triangle, the standard notation used in Trigonometry.

4. May 11, 2017

Buffu

$\displaystyle {c \over \sin c} = 2R$

Check your work again, you replace $\sin c$ with $a/(2R)$, you should do $c/(2R)$

5. May 11, 2017

Wrichik Basu

You are wrong: $$\frac {c} {\sin (c)} = 2R$$ not $$\frac {c}{\sin ^2 (c)} = 2R$$

Last edited by a moderator: May 11, 2017
6. May 11, 2017

Buffu

Yes, that was a typo.

Last edited by a moderator: May 11, 2017
7. May 11, 2017

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.

8. May 12, 2017

Wrichik Basu

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.