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    Question

    cosx/(1 – sinx) + cosx/(1+ sinx) = 4, 0 o 

    x < 90 o , then the value of (tanx + cosecx)
    A 7√3/3 Correct Answer Incorrect Answer
    B 5√3/3 Correct Answer Incorrect Answer
    C 3√3/3 Correct Answer Incorrect Answer
    D 5√2/2 Correct Answer Incorrect Answer

    Solution

    cosx/(1 – sinx) + cosx/(1 + sinx) = 4
    cosx(1 + sinx) + cosx(1 – sinx) = 4(1 – sin 2 x)
    cosx + cosxsinx + cosx – cosxsinx = 4cos 2 x
    2cosx = 4cos 2 x
    cosx = 1/2
    So, x = 60 o
    tanx + cosecx = √3 + 2/√3 = 5√3/3

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