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
  1. Equilateral
  2. Right angled
  3. Isosceles but not equilateral
  4. 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.

Asked in: AP EAMCET 2020 (18 Sep Shift 2)

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