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Help with Trigonometry

  1. Sep 4, 2008 #1
    1. The problem statement, all variables and given/known data
    If [tex]tan x =\frac{2b}{a-c}[/tex]
    [tex]y=a.cos^{2} x + 2b.sin x.cos x+ c.sin^{2} x[/tex]



    [tex]z=a.sin^{2} x - 2b.sin x.cos x+ c.cos^{2} x[/tex]


    Prove y-z=a-c
    3. The attempt at a solution

    Assuming that the result to be proved is true;

    add y and z
    y+z=a+c
    and from the result to be proved
    y-z=a-c
    From this:
    y=a
    and
    z=c

    But can it be proved using the first equation of tan x ????? I tried a lot but i couldnt do it.
     
  2. jcsd
  3. Sep 4, 2008 #2

    Dick

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    Re: Trigonometry

    Sure. Use the first equation to say 2b=(a-c)*tan(x). Substitute that for the 2b's in the other two equations.
     
  4. Sep 4, 2008 #3

    CompuChip

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    Re: Trigonometry

    First of all, you cannot assume what you want to prove. For example, I can prove 1 = 0 that way:
    Code (Text):
    Assume that 1 = 0 (which we want to prove) is true.
    Then also 0 = 1.
    Add them: 1 = 1.
    This is a true equation, QED
    .

    Secondly, if you assume y-z=a-c, then why do you conclude y = a and z = c and even if this where true (which it's not) how would this help the proof?

    You will have to work from the given information. First work out what y - z is. Then you can use the first equation of tan(x) to replace b by something in terms of a, c and x. Finally, use some more trig identities to get to a - c.
     
  5. Sep 5, 2008 #4
    Re: Trigonometry

    Thanks friend. It was silly of me to have not noticed that. Thanks a lot once again.
     
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