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    Question

    If p cos A = 2q sin A and 2p cosec A – q sec A = 3,

    then the value of p² + 4q² is:
    A 2 Correct Answer Incorrect Answer
    B 4 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D 3 Correct Answer Incorrect Answer

    Solution

    p cosA = 2q sinA tanA = p/2q Also, 2p cosecA - q secA = 3 2p/sinA - q/cosA = 3 Multiply by sinA cosA:  2p cosA - q sinA = 3sin A cosA Substitute p cosA = 2q sinA, we get So, 3q sinA = 6q sin2A/p 3p sinA = 6sin2A p = 2sinA Now from p cosA = 2q sinA 2sinA . cos A = 2q sinA cosA = p/2, cos A = q (p/2)2 + q2 = 1 p2/4 + q2 = 1 Multiply by 4, p2 + 4q2 = 4

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