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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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