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    Question

    If 7cos²A + 2sin²A = 6, then find the value of (sec²A -

    1)
    A 1/3 Correct Answer Incorrect Answer
    B 1/4 Correct Answer Incorrect Answer
    C 2/5 Correct Answer Incorrect Answer
    D 1/5 Correct Answer Incorrect Answer

    Solution

    7cos²A + 2sin²A = 6
    Or, 5cos²A + 2cos²A + 2sin²A = 6
    Or, 5cos²A + 2(cos²A + sin²A) = 6
    Or, 5cos²A + 2 = 6 (Using, cos²A + sin²A = 1)
    Or, 5cos²A = 4
    Or, cos²A = 4/5
    So, sec²A = 5/4 (sec A is reciprocal of cos A)
    Required value = 5/4 - 1 = 1/4

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