limx→−1 cos⁡2−cos⁡2xx2−|x| is equal to 

limx1cos2cos2xx2|x| is equal to 

  1. A

    2

  2. B

    sin 2

  3. C

    2 sin2

  4. D

    none of these 

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    Solution:

    We have,

    limx1cos2cos2xx2|x|=limx12sin(1+x)sin(x1)x2+x [|x|=x for x<0]=2limx1sin(x+1)x+1×sin(x1)x=2×1×sin(2)(1)=2sin2.

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