Total number of solutions of the equation 3x+2tan⁡x=5π2 in x∈[0,2π] is equal to

    Total number of solutions of the equation 3x+2tanx=5π2 in x[0,2π] is equal to

  1. A

    1

  2. B

    2

  3. C

    3

  4. D

    4

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    Solution:

    We have, 3x+2tanx=5π2

     tanx=5π43x2

    Let   5π43x2=y

    and  y=tanx

     Graph of y=5π43x2 and y=tanx meet exactly three times in [0,2π].Thus,

       the number of solutions of given equation is 3.

     

     

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