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Help on tough trig/algebra problem

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Constants a,b,c,d

    2. Relevant equations

    a/((1-b*cos(x))^1) + c = cos(x+d)/(1-b*cos(x)), solve for x

    3. The attempt at a solution

    I've tried many different forms and substutions to try to factor this puppy and get 2 solutions. The expanded equation, after using the cos sum identity, looks like

    p*cos(x)^2 + q*cos(x) + r*sin(x) + s*sin(x)*cos(x) = t

    I attempted to eliminate the equation by multiplying t by sin(x)^2+cos(x)^2 and finding some common terms but so far that hasn't helped. I've also trying substituting all the half and double angle identities I know and haven't been able to come up with anything. I know this doesn't show much work, but I have spent a lot of time on this, so any help is much appreciated!
     
  2. jcsd
  3. Nov 10, 2012 #2

    Mark44

    Staff: Mentor

    Why do you have an exponent of 1 on the left side? Did you leave something out?
     
  4. Nov 10, 2012 #3
    Yes, thanks. That is a 2. Pretty significant typo :)

    a/((1-b*cos(x))^2) + c = cos(x+d)/(1-b*cos(x)),
     
  5. Nov 10, 2012 #4

    haruspex

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    You could manipulate it into the form sin(x) = f(cos(x)) then square both sides, substituting 1-cos2(x) on the left. I think that will give you a quartic in cos(x). Not pretty.
     
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