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AP EAMCET20224 Jul 2022Morning ShiftMathematicsDeterminantsActual

Let A = 5 sin 2 θ cos 2 θ - sin 2 θ - 5 1 cos 2 θ 1 5 . Then maximum value of det A is

Options

  1. A- 125
  2. B200
  3. C- 255 2
  4. D145

Correct answer

A. - 125

Step-by-step solution

A = 5 sin 2 θ cos 2 θ - sin 2 θ - 5 1 cos 2 θ 1 5 A = 5 - 26 - sin 2 θ - 5 sin 2 θ + cos 2 θ + cos 2 θ - sin 2 θ + 5 cos 2 θ = - 130 + 5 sin 4 θ - sin 2 θ cos 2 θ - sin 2 θ cos 2 θ + 5 cos 4 θ = - 130 + 5 sin 4 θ + cos 4 θ - 2 sin 2 θ cos 2 θ = - 130 + 5 sin 2 θ + cos 2 θ 2 - 2 sin 2 θ cos 2 θ - 2 sin 2 θ cos 2 θ = - 125 - 12 sin 2 θ cos 2 θ = - 125 - 3 2 sin θ cos θ

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