Question

In a \( \triangle ABC \), if
\( \dfrac{\cos A}{a} = \dfrac{\cos B}{b} = \dfrac{\cos C}{c} \),
and the side \( a = 2 \), then area of triangle is:

• A. 1
• B. 2
• C. \(\dfrac{\sqrt3}{2}\)
• D. \sqrt3

Hint:

Symmetric trigonometric ratios often indicate an equilateral triangle.

Answer 1

The Correct Option is C

Step 1: Given condition implies triangle is equilateral. 

Step 2: Hence \( a = b = c = 2 \). 

Step 3: Area of equilateral triangle:
\( \dfrac{\sqrt{3}}{4} a^2 = \dfrac{\sqrt{3}}{4} \cdot 4 = \dfrac{\sqrt{3}}{2} \)