A problem in Trigonometry (Properties of Triangles) v2

[Wrichik Basu]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Buffu]

Homework Statement

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

Homework Equations

The Attempt at a Solution

View attachment 203380

What is $\Delta$ ?

 

[Wrichik Basu]

What is $\Delta$ ?

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

 

[Buffu]

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

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

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

 

[Wrichik Basu]

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

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

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

 

[Buffu]

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

Yes, that was a typo.

 

[Mark44]

What is Δ ?

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

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.

 

[Wrichik Basu]

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.

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.