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Simplify the expression (i have a test tomorrow)

  1. Oct 24, 2007 #1

    PHK

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    1. The problem statement, all variables and given/known data
    sec+csc/1+tan





    3. The attempt at a solution

    i tried simplifying it and the farthest i got was: 1/cos + 2/sin + cos/sin^2
    im not sure thats even right
     
  2. jcsd
  3. Oct 24, 2007 #2
    ok i'm a bit confused on what your problem is ... plz make it a lil more clear
     
  4. Oct 24, 2007 #3

    PHK

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    i have to simplify sec+csc/1+tan
     
  5. Oct 24, 2007 #4
    the problem is ...

    [tex]\sec{x}+\frac{\csc{x}}{1}+\tan{x}[/tex]

    why did you write the 1 ... ?
     
  6. Oct 24, 2007 #5

    PHK

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    its not that its, sec+csc and all that over 1+tan. sec+csc
    ...................................................................1+tan


    ignore the the dots the problem i am and talking about is in the the top right

    also (sec+csc)/(1+tan)
     
  7. Oct 24, 2007 #6

    cristo

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    You should use parentheses to make your questions unambiguous in future. Also, note that sec doesn't mean anything; you mean sec(x). Ok, well you could write everything in terms of sines and cosines first. Just substitute into that expression, then try and tidy up.
     
  8. Oct 24, 2007 #7
    (sec+csc)/(1+tan) ... much clearer

    hopefully you see why i was confused, if you want help you gotta be clear! or we're gonna be going back and forth w/o you ever receiving help. lol
     
  9. Oct 24, 2007 #8

    dynamicsolo

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    How are each of these trig functions defined? Replace each one by its definition and see what you get when you add the appropriate fractions.
     
  10. Oct 24, 2007 #9

    PHK

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    yea sorry for not being clear.

    and i already tryed replacing them by the definition. i just end up with 1/cos + 2/sin + cos/sin^2
     
  11. Oct 24, 2007 #10
    what did you multiply by?

    i multiplied both NUM and DEN by cosx

    i don't really see what else can be done.
     
  12. Oct 24, 2007 #11

    dynamicsolo

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    I don't see how you got 2/sin, but I can tell you that this simplifies a lot.

    Just make the replacements first, then add the fractions in the numerator and in the denominator separately. You'll have a compound fraction, where you can then invert the denominator and multiply. You'll see a couple of things that you can then cancel.

    [ (1/cos) + ? ] / [ 1 + ? ] = ?
     
  13. Oct 24, 2007 #12

    PHK

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    maybe thats wrong then (1/cos + 2/sin + cos/sin^2), also i tried multiplying by cosx and i get 1/sin + cos - 1/cos i tried going further but it seems like im doing something wrong. does anyone have the solution yet?
     
  14. Oct 24, 2007 #13
    [tex]\frac{\sec + \csc}{1+\tan}=\frac{\frac{1}{\cos} + \frac{1}{\sin}}{1+\frac{\sin}{\cos}}=\frac{\frac{\sin + \cos}{\cos \sin}}{\frac{\cos+\sin}{\cos}=\frac{1}{\sin}=\csc[/tex]
     
  15. Oct 24, 2007 #14

    dynamicsolo

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    The next step should be

    [ (1/cos) + (1/sin) ] / [ 1 + (sin/cos) ] . Add the fractions in the numerator and in the denominator, then simplify the compound fraction you get.

    The answer is csc x .
     
  16. Oct 24, 2007 #15

    PHK

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    [ (1/cos) + (1/sin) ] / [ 1 + (sin/cos) ] thats the original problem. how did you get csc from that?
     
  17. Oct 24, 2007 #16

    dynamicsolo

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    Having looked at your source code, I think I should say that you should resist the temptation to provide the full solution to a problem. This forum is intended to guide students, rather than simply hand them the answers...
     
  18. Oct 24, 2007 #17

    dynamicsolo

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    What does you get when you add (1/cos) + (1/sin) ? How about 1 + (sin/cos) ?
     
  19. Oct 24, 2007 #18

    PHK

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    oh i get it thanks i was adding the top part properly but not hte bottm part. thanks
     
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