Let $A, B$ and $C$ be three angles of a $\triangle A B C$ such that $\cos A+\cos B+\cos C=\frac{3}{2}$, then the $\triangle A B C$ is

Question

Let $A, B$ and $C$ be three angles of a $\triangle A B C$ such that $\cos A+\cos B+\cos C=\frac{3}{2}$, then the $\triangle A B C$ is, Equilateral, Right angled, Isosceles but not equilateral, Scalene

MARKS App · Accepted Answer

Given, $\cos A+\cos B+\cos C=\frac{3}{2}$ Above equation is possible only for $A=B=C=\frac{\pi}{3}$ $\therefore \triangle A B C$ is equilateral, Hence, option (a) is correct.

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