Q120 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

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

  • Correct answer
    A
    Equilateral
  • B
    Right angled
  • C
    Isosceles but not equilateral
  • D
    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.

Hence, the correct answer is option: 'A'.

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