If a1,a2,…,an  are in AP  with common  difference  d, then the  sum of the  series sind cosec ⁡a1cosec ⁡a2+cosec ⁡a2cosec ⁡a3+…+cosec⁡an−1cosec⁡an is 

If a1,a2,,an  are in AP  with common  difference  d, then the  sum of the  series sind cosec a1cosec a2+cosec a2cosec a3++cosecan1cosecan is
 

  1. A

    seca1secan

  2. B

    cota1cotan

  3. C

    tana1tanan

  4. D

    coseca1cosecan

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    Solution:

    Since,a1,a2,a3,,an are in AP

     d=a2a1=a3a2==anan1

    sindcoseca1coseca2++cosecan1cosecan=sina2a1sina1sina2++sinanan1sinan1sinan=sina2cosa1cosa2sina1sina1sina2++sinancosan1+cosansinan1sinan1sinan

    =cota1cota2+cota2cota3   ++cotan1cotan

    =cota1cotan

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