Mathematics - Properties of Triangles Question with Solution | TestHub

$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$ $\Rightarrow \frac{\cos \mathrm{A}}{2\mathrm{R}\sin \mathrm{A}}=\frac{\cos \mathrm{B}}{2\mathrm{R}\sin \mathrm{B}}=\frac{\cos \mathrm{C}}{2\mathrm{R}\sin \mathrm{C}}$ $\Rightarrow \cot A=\cot B=\cot C$ $\Rightarrow \mathrm{A}=\mathrm{B}=\mathrm{C}=60^{\circ }\Rightarrow \Delta \mathrm{ABC}$ is equilateral Hence, area of $\Delta =\frac{\sqrt{3}}{4}{\mathrm{a}}^2=\sqrt{3}$.