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      Question

      If 8cos 2  A + 3sin 2  A = 9, then

      calculate the value of (sec 2  A - 1).
      A -1/6 Correct Answer Incorrect Answer
      B -5/6 Correct Answer Incorrect Answer
      C 1/6 Correct Answer Incorrect Answer
      D 5/6 Correct Answer Incorrect Answer

      Solution

      8cos 2  A + 3sin 2  A = 9

      Or, 5cos 2  A + 3cos 2  A + 3sin 2  A = 9

      Or, 5cos 2  A + 3 X (cos 2  A + sin 2  A) = 9

      Or, 5cos 2  A + 3 = 9 (Using, cos 2  A + sin 2  A = 1)

      Or, 5cos 2  A = 6

      Or, cos 2  A = (6/5)

      So, sec 2  A = (5/6) (sec X is reciprocal of cos X)

      Required value = (5/6) - 1 = (- 1/6)

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