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Proving a Sinh(x) expression to be an integer

  1. Sep 16, 2009 #1
    Prove or disprove: sinh2(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex])) is an integer


    Obviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though.

    3. The attempt at a solution

    I've tried rewriting sinh2 as (1/4)(e2x+e-2x-2) and after all the substitutions and log rules I get (1/4)(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex])+1/(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex]))-2)

    what now?....
     
  2. jcsd
  3. Sep 16, 2009 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Use the identity

    [tex]
    \exp{(\ln{x})}=x
    [/tex]

    to eliminate exp and ln.

    ehild
     
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