JEE Advance - Mathematics (1984 - No. 32)
For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilateral.
The given condition implies A = B = C = 60 degrees, hence the triangle is equilateral.
The given condition is impossible, no such triangle exists.
The given condition implies the triangle is isosceles, but not necessarily equilateral.
The given condition only implies the triangle is acute.
The given condition implies the triangle is right angled.