Question

In a $\triangle A B C$ $\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}$ and $a = 2,$ then the area of a triangle is

• A. 1
• B. 2
• C. $\frac{\sqrt{3}}{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (D)

$\sqrt{3}$

Answer 2

By sine rule, $\tan A = \tan B = \tan C$; $\therefore$ Triangle is equilateral .

Hence, $\Delta = \frac{1}{2}.a.a.\sin 60^{o} = \frac{1}{2}.2.2.\frac{\sqrt{3}}{2} = \sqrt{3}$.