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Verify a simplification with trig identity

  1. Jan 10, 2004 #1
    After a little calculus and lots of algebra I get the expression

    cot(2la) = (l^2 - k^2) / (2kl)

    it is suggested to simplify with the trig identity

    tan(t/2) = sqrt(1 + cot^2(t) ) - cot(t)

    when I do so, I get

    tan(la) = k/l

    notice that we have gone from cot(2la) to tan(la). The text I am reading says

    tan(la) = l/k

    which I think is wrong. Can someone else please give it a try?

    the key step was combining the 1 + cot^2(t) over a common denom.
     
  2. jcsd
  3. Jan 11, 2004 #2
    i believe u might have missed out at other roots I get both -l/k as well as k/l

    [tex]cot2la=\frac{1-tan^22la}{2tanla}=\frac{l^2-k^2}{2kl}[/tex]

    After rearrangement u will get

    [tex]kltan^2la+(l^2-k^2)tanla-kl=0[/tex]

    so two roots will be given by

    [tex]tanla=\frac{-(l^2-k^2) \pm \sqrt{(l^2-k^2)^2+4k^2l^2}}{2kl}[/tex]

    After solving u will get the 2 roots

    [tex]tanla = \frac{k}{l} \ & \ -\frac{l}{k}[/tex]
     
    Last edited: Jan 11, 2004
  4. Jan 11, 2004 #3
    Thanks. There is a second root but on that one the book & I agree so I assumed I was correct. :smile:

    Also, I like you method better than the obscure substitution suggested by the book.
     
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