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AP EAMCET202120 Aug 2021Morning ShiftMathematicsDeterminantsActual

If A , B , C are the angles of a triangle then the system of equations - x + y cos C + z cos B = 0 , x cos C - y + z cos A = 0 , x cos B + y cos A - z = 0 have

Options

  1. Aonly zero solution
  2. Ba non-zero solution for all triangles ∆ A B C
  3. Conly zero solution but for certain values of A ,   B ,   C
  4. Da non-zero solution if ∆ A B C is an equilateral triangle & not for all triangles

Correct answer

D. a non-zero solution if ∆ A B C is an equilateral triangle & not for all triangles

Step-by-step solution

A , B , C are angles of triangle. - x + y cos C + z cos B = 0 x cos C - y + z cos A = 0 x cos B + y cos A - z = 0 A = - 1 cos C cos B cos C - 1 cos A cos B cos A - 1 A = - 1 1 - cos 2 A - cos C - cos C - cos A . cos B + cos B cos A . cos C + cos B A = - 1 + cos 2 A + cos 2 C + cos A . cos B . cos C + cos A . cos B . cos C + cos 2 B ∵ A , B ,   C are angles of triangle. So, A = 0 for equilateral triangle and A ≠ 0 for all other triangles. Hence, a non-zero solution if △ A B C is an equilateral

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