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    Question

    If 2x = cosec @ and 4/x = cot @ then the value of 2(x ²

    - 1/x ² ) is
    A 1/2 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 8 Correct Answer Incorrect Answer

    Solution

    2x = cosec@ .............(i) 2/x = cot  @ ...............(ii) adding (i) and (ii), we get 2 (x + 1/x) = cosec  @ + cot  @ ...........(iii) subtracting (ii) from (i), we get 2 (x - 1/x) = cosec  @ - cot  @ ..............(iv) Multiply (iii) and (iv), we get 4 (x 2  - 1/x2) = cosec2   @ - cot 2   @  2(x2  - 1/x2  ) = 1/2 

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