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Homework Help: Find solution of eqation 2cot^2x-5cosec x =1

  1. Mar 25, 2012 #1
    2cot2(x)-5cosec(x)=1 for exactly 6 values of x belongs to [0,nπ], then find the minimum value of n.
    my answer is 5.
    How i did it.changing cot to cosec and then solving equation it will give something like cosec(x)=3. for x belongs to 0 to 5π it has 6 solutions..
    this is question of a class test & answer in test's answer sheet is 6.
    WHO IS correct. me or answer sheet???????
  2. jcsd
  3. Mar 25, 2012 #2


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    In 2π, you'd get 2 solutions A and 180-A. So for the next 2π, you'd have 4 in total and then in 2π again, you'd get 6.

    So your range would be 6π.
  4. Mar 25, 2012 #3
    If i have got A and 180-A then i have got solutions in [0,π] not [0,2π] and in next 2π(or in [0,3π]) i will have 4 solution why i should go for 4π. similarly for next 5π.
    Last edited: Mar 25, 2012
  5. Mar 25, 2012 #4


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    You are correct for the problem that was given.

    There are two roots in [0, π] ,

    two roots in [2π, 3π] ,

    and two roots in [4π, 5π] .
  6. Mar 25, 2012 #5
    thanks sammy..
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