- #1

Saitama

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## Homework Statement

In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx).

## Homework Equations

## The Attempt at a Solution

The usual notation is:

a,b,c are three sides of the triangle opposite to the angles A,B and C respectively.

I remember a formula relating ∆ and the three sides i.e

$$\Delta=\frac{abc}{4R} \Rightarrow abc=4R \Delta$$

Also, from the law of sines,

$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$$

where R is the circumradius of triangle.

The given expression can be written as:

$$2a^2b^2c^2 (\sin A \cos A + \sin B \cos B + \sin C \cos C)$$

I can substitute abc and sines from the above two relations but what should I replace cosines with? Law of cosines doesn't seem to be of much help.

Any help is appreciated. Thanks!