If  a1,a2,…,an are in A.P., with common difference  d≠0 then sum of the series sin⁡dcosec⁡a1coseca2+cosec⁡a2cosec⁡a3+…+cosec⁡an−1cosec⁡anis 

If  a1,a2,,an are in A.P., with common difference  d0 then sum of the series sindcoseca1coseca2+coseca2coseca3++cosecan1cosecanis 

  1. A

    seca1secan

  2. B

    coseca1cosecan

  3. C

    cota1cotan

  4. D

    tana1tanan

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    Solution:

    sindcoseca1coseca2+coseca2coseca3++cosecan1cosecan

    =sina2a1sina1sina2+sina3a2sina2sina3++sinanan1sinan1sinan=cota1cota2+cota2cota3++cotan1cotan=cota1cotan

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