If 16sin⁡x,cos⁡x,tan⁡x  are in G.P., then r is equal to

If 16sinx,cosx,tanx  are in G.P., then r is equal to

  1. A

    nπ±π3,nZ

  2. B

    2nπ±π3,nZ

  3. C

    nπ+(1)nπ3,nZ

  4. D

    none of these

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    Solution:

    It is given that 16sinx,cosx,tanx are in GP

     cos2x=16sinx tanx

    6cos2x=sinx tanx

     6cos3x+cos2x1=0 cosx126cos2x+4cosx+2=0

     cosx=12cos2x+4cosx+2=0 has imaginary roots 

     cosx=cosπ3 x=2nπ±π3,nZ.

     

     

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