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    Question

    Suppose 140sin²X + 124cos²X = 136 and 184sin²Y +

    200cos²Y = 196, then determine the value of 18cosec²Xsec²Y.
    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, 140sin²X + 124cos²X = 136

    So, 124(sin²X + cos²X) + 16sin²X = 136

    Or, 16sin²X = 12

    Or, sin²X = 12/16 = 3/4

    Or, sinX = √3/2

    So, X = 60⁰

    Similarly, Y = 30⁰

    So, 18cosec²Xsec²Y = 18 × 4/3 × 4/3 = 32

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