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Math Help - How to solve this?

  1. #1
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    Cool How to solve this?

    If n ∈ N, solve the equation cos*n x − sin*n x = 1, for x ∈ R.
    *n means exponent
    ∈ means member of

    I have no clue how to solve this.

    Thanks in advance!
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Think about this.

    If x = 0 , then the solution is n \in \mathbb{Z}^+
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  3. #3
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    Sorry, that just went over my head?
    I know this is simple but i'm not getting the concept here :/
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  4. #4
    MHF Contributor

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    Pickslides is saying that for x= 0, cos(x)= cos(0)= 1, sin(x)= sin(0)= 0 and the equation is true for n any positive integer (actually it is true for any integer).

    But the problem here is to determine those positive integers, n, such that the equation is true for all x. More to the point would be to look at x= \pi/4 for which cos(x)= sin(x).
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  5. #5
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    Thanks! Got it
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