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Simplify cofunction expression

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    csc(pi/2-x)/cos(x+pi/2) + cot(pi/2-x)

    3. The attempt at a solution

    1/cosx/-sinx + sinx/cosx

    -1/sinxcosx+ sinx/cosx(sinx/sinx)

    (sin2x - 1) / sinxcosx

    -cos2x/sinxcosx

    -cosx/sinx

    -cotx

    is this right the answer key says it is cosx but that could be wrong I have done this a couple times and gotten the same answer
     
  2. jcsd
  3. Apr 24, 2009 #2

    rock.freak667

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    Homework Helper

    I don't think it can be the same as cosx because if you put x=0, it doesn't work.
     
  4. Apr 24, 2009 #3
    I'm assuming you mean (1/cosx)/-sinx in the first fraction. Anyway, this is not correct.


    01
     
  5. Apr 25, 2009 #4
    (1) cofunction%20identiies%20csc%20sec.gif

    (2)cos(x+pi/2) = - sinx

    (1)/(2)=

    secx/-sinx=

    (1/cosx)/-sinx

    what is wrong about that?
     
  6. Apr 25, 2009 #5
    Oops, sorry about that. I misread the problem. I redid the problem and now I'm getting -cot x. You sure you copied the problem correctly?


    01
     
  7. Apr 25, 2009 #6
    Well the way it is written is the csc cofunction is directly above the cos cofunction and then added to the cot cofunction. There isn't actually a line between the two. I am sure i am meant to divide the two but is there anything else that could mean. FYI my instructor is very smart but he is also somewhat absent minded and I am pretty sure he put together these practice assignments himself he could have made a mistake it wouldn't be the first time.
     
  8. Apr 25, 2009 #7

    jhae2.718

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    Gold Member

    Assuming the original problem was copied correctly, I would say that you are correct; I get -cot(x) when I solve the problem. In addition I graphed the two curves as a check and they are the same...
     
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