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An expression equivalent to [cos(x)+sin(x)]/[cos(x)+sin(x)]

  1. Feb 9, 2005 #1
    I have this question --> [tex] \frac {\cos (x) + \sin (x)} {\cos (x) - \sin (x)} [/tex] how do you find an expression that is eqivalent to this using trig identities? I have no clue every time I do this problem the top and bottom cancel out plus none of the terms can be replaced with trig identities, can somone plz help me out ? :eek:
     
  2. jcsd
  3. Feb 9, 2005 #2

    Galileo

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    You could multiply the top and bottom by cos x+sin x.
    Then use some trig identities like [itex]\sin^2x+\cos^2x=1[/itex] upstairs and downstairs. Then you can simplify is further by using 2 other trig id's.
    Look up the table. :)
     
  4. Feb 10, 2005 #3

    Can I ask what table? :smile:
     
  5. Feb 10, 2005 #4

    xanthym

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    Try what the previous msg suggested:
    a) Multiply Numerator & Denominator by:
    [tex] cos(\theta) + sin(\theta) [/tex]
    b) Use Identities Like:
    [tex] sin^2(\theta) + cos^2(\theta) = 1 [/tex]
    [tex] sin(2\theta) = 2sin(\theta)cos(\theta) [/tex]
    [tex] cos(2\theta) = cos^2(\theta) - sin^2(\theta) [/tex]
    Also check the following Trig Identity Table:
    http://www.math2.org/math/trig/identities.htm

    ~
     
  6. Feb 10, 2005 #5
    why not try tan ?
     
  7. Feb 10, 2005 #6

    xanthym

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    Yes. The tan() and sec() would be next. (Needed to leave something for the reader to discover!!)

    ~
     
    Last edited: Feb 10, 2005
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