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Tigonometric Identies problem help!

  1. Oct 30, 2004 #1
    I need hep verifying two trig identity problems

    1. (cot-csc)^2 = (1-cos)/(1+cos)


    2. sin2tan2/tan2-sin2 = 1

    Any help?
    Thanks in advance!
     
  2. jcsd
  3. Oct 30, 2004 #2

    Dr Transport

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    The easiest way to prove trig identities is to express all of the quantites in terms of sines and cosines, then start rearranging from there......
     
  4. Oct 30, 2004 #3
    I have tried doing that many times ..still having no luck..
     
  5. Oct 31, 2004 #4

    James R

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    Could you please write out your questions again, with the variables, and all bracketing correct?

    There's no way to tell is, by sin2 you mean (sin x)<sup>2</sup> or sin 2x.

    Also, in your second problem, do you mean

    [tex]\frac{\sin^2 x \tan^2 x}{\tan^2 x} - \sin^2 x[/tex]

    or something else?

    Notation is important.
     
  6. Oct 31, 2004 #5

    James R

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    Here's a solution to the first problem:

    [tex](\cot x - \mbox{cosec} x)^2\\
    = \left(\frac{\cos x}{\sin x} - \frac{1}{\sin x}\right)^2\\
    = \frac{(\cos x - 1)(\cos x - 1)}{\sin^2 x}\\
    = \frac{(\cos x - 1)(\cos x - 1)}{1 - \cos^2 x}\\
    = \frac{(\cos x - 1)(\cos x - 1)}{(1 + \cos x)(1 - \cos x)}\\
    = \frac{1 - \cos x}{1 + \cos x}[/tex]
     
    Last edited: Oct 31, 2004
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