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Please help me with this problem

  1. Mar 24, 2016 #1
    1. The problem statement, all variables and given/known data
    cos(θ)^x+sin(θ)^x=1
    find the number of real values of x satisfying this equation


    2. Relevant equations
    none


    3. The attempt at a solution
    the answer given is 1 which is 2.which is obvious but i don't know how to prove that it is the only solution available
     
    Last edited by a moderator: Mar 25, 2016
  2. jcsd
  3. Mar 25, 2016 #2

    Nathanael

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    Homework Helper

    You want to prove there is no x, other than 2, which gives equality for all values of θ.

    Choose any particular θ and show that the only x-value for that particular θ which gives equality is x=2 (that would prove it, right?)

    What particular value of θ might it be easy to show this for?
     
  4. Mar 25, 2016 #3
    thank you for replying sir,i want to prove that 2 is the only solution possible.
     
  5. Mar 25, 2016 #4

    Nathanael

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    When you say "the only solution possible," what you really mean is, "the only solution possible for all values of θ" right?

    If you were to choose a particular value of θ and prove that 2 is the only solution for that θ, then that would prove what you want, because if x is not 2 then x does not solve it for that particular θ you chose.
    This means you only have to prove it for any single value of θ. Do you agree?

    I didn't want to hint at it too much, but if you choose the θ such that cosθ=sinθ then you can factor together the exponent x and complete the proof.
     
  6. Mar 25, 2016 #5
    thank you sir, from there i will try on my own
     
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