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Cosine and Tangent

  1. Jun 17, 2011 #1
    Demontration of:
    cos(x)² =
    1
    [itex]\overline{1+tan(x)²}[/itex]

    Anyone know?

    If you don't understand:

    cos(x)² = 1/1+tan(x)²
     
  2. jcsd
  3. Jun 17, 2011 #2

    lavinia

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    what have you tried?
     
  4. Jun 17, 2011 #3
    I need a demonstration of how to get this formula
     
  5. Jun 17, 2011 #4

    HallsofIvy

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    Why? Wouldn't it be better to find such a demonstration yourself?

    As a hint, look at a standard identity involving [itex]tan^2(x)[/itex].
     
  6. Jun 17, 2011 #5
    I tried to find, but fail =/
     
  7. Jun 17, 2011 #6

    micromass

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    What is the definition of the tangent?
     
  8. Jun 17, 2011 #7
    no... the demonstration of the formula..
     
  9. Jun 17, 2011 #8

    micromass

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    I'm trying to find the demonstration together with you! What is the tangent?
     
  10. Jun 17, 2011 #9
    x? lol '-'
     
  11. Jun 17, 2011 #10

    micromass

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    Wait, so you ask us how to prove this formula, and you don't even know what a tangent is? I suggest looking up the definitions and the formulas and then come back.
     
  12. Jun 17, 2011 #11
    I don't understand your question sorry '-'...

    tan(x) = sin(x)/cos(x)..
     
  13. Jun 17, 2011 #12

    micromass

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    Yes, tan(x)=sin(x)/cos(x).

    Now plug that in into the equation

    [tex]\cos^2(x)=\frac{1}{1+\tan^2(x)}[/tex]

    and simplify the right-hand side.
     
  14. Jun 17, 2011 #13
    cos²(x)+sin²(x) = 1

    That?
     
  15. Jun 17, 2011 #14

    Mark44

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    Start with 1/(1 + tan2(x)), and replace the tangent term. Simplify the result.
     
  16. Jun 17, 2011 #15

    tiny-tim

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    ok, so how can you get from that back to the original equation? :smile:
     
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