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      Question

      Suppose 140sinĀ²X + 124cosĀ²X = 136 and 184sinĀ²Y +

      200cosĀ²Y = 196, then determine the value of 18cosecĀ²XsecĀ²Y.
      A 16 Correct Answer Incorrect Answer
      B 22 Correct Answer Incorrect Answer
      C 28 Correct Answer Incorrect Answer
      D 32 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Since, 140sinĀ²X + 124cosĀ²X = 136

      So, 124(sinĀ²X + cosĀ²X) + 16sinĀ²X = 136

      Or, 16sinĀ²X = 12

      Or, sinĀ²X = 12/16 = 3/4

      Or, sinX = āˆš3/2

      So, X = 60ā°

      Similarly, Y = 30ā°

      So, 18cosecĀ²XsecĀ²Y = 18 Ɨ 4/3 Ɨ 4/3 = 32

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