Let \(A, B\) and \(C\) be three angles of a \(\triangle A B C\) such that \(\cos A+\cos B+\cos…
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
Solution
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.