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Trig Simplification

  1. Oct 30, 2008 #1
    I need to somehow simplify:



    [tex] B=\sqrt{\frac{2}{L}}\sqrt{\frac{\beta}{1+\beta}} [/tex]


    [tex]\alpha=\frac{L}{2}k_2 [/tex] and [tex]\beta=\frac{L}{2}k_1 [/tex]

    And [tex]\beta[/tex] is also defined transcendentally:


    Any ideas would be appreciated, I see no way of getting rid of the trig functions. I've tried looking for identities and even given it to mathematica; it seems to me I'm missing some sort of special trick.
    Last edited: Oct 31, 2008
  2. jcsd
  3. Oct 31, 2008 #2


    Staff: Mentor

    Is it a typo that alpha and beta are equal? It seems an unnecessary complication to add another variable if it's not needed. Otherwise I would just start substituting things into the right side of your first equation and see where that takes me.
  4. Oct 31, 2008 #3
    Ah, it is... thanks, it's fixed now alpha should be (L/2)*k2
  5. Oct 31, 2008 #4


    Staff: Mentor

    Now replaces cos(2 alpha) and sin(2 alpha) using the double-angle identities, and use your other two relationships to get rid of alpha to see if you can make the right side look like the left.
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