The value of limx→0 1+tan⁡x1+sin⁡xcosec⁡x, is

The value of limx01+tanx1+sinxcosecx, is

  1. A

    1

  2. B

    e

  3. C

    e-1

  4. D

    none of these 

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    Solution:

    We have, 

    limx01+tanx1+sinxcosecx=limx0(1+tanx)cosecx(1+sinx)cosecx=elimx0tanxcosecx limx0sinx(cosecx) =e1×e1=e1×e1=e0=1

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