In a ∆ABC, if

In a $\Delta A B C$

Given $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c} \ldots(1)$ and $a=2$

Using sine formula 

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \quad \ldots(2)$

using above two, (1) and (2)

we get,

$\frac{\cos A}{\sin A}=\frac{\cos B}{\sin B}=\frac{\cos C}{\sin C}$

$\Rightarrow \cot A=\cot B=\cot C$

$\Rightarrow$ angle $A=B=C=60^{\circ}$

$\Rightarrow \triangle A B C$ is an equilateral triangle

$\therefore$ Area of triangle $\mathrm{ABC}=\frac{\sqrt{3}}{4} a^{2}$

$=\frac{\sqrt{3}}{4} \times 4$

$=\sqrt{3}$ unit $^{2}$

or $\sqrt{3}$ Sq. unit