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    Question

    If cosec [180° − (3q/2) ] = √2, 0° < q < 90°, then

    find the value of {(2/√3) X cos q - 4 cos 3q}.
    A √3/2 Correct Answer Incorrect Answer
    C 2 Correct Answer Incorrect Answer
    D 1 Correct Answer Incorrect Answer

    Solution

    cosec [180° − (3q/2) ] = √2

    Or, cosec (3q/2) = cosec 45 o  [because cosec 45 o  = √2, and cosec (180 - q) = cosec q]

    Or, (3q/2) = 45 o

    Or, q = 45 o  X (2/3)

    So, q = 30 o

    (2/√3) cos q - 4 cos 3q = (2/√3) cos 30 o  - 4 cos (3 X 30 o )

    = (2/√3) X (√3/2) - 0 (because, cos 30 o  = (√3/2) and cos 90 o  = 0)

    = 1

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