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Homework Help: Calc- prove sinh(x) and cosh(x) identities?

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove

    cosh(2x)= cosh^2(x) + sinh^2(x)


    2. Relevant equations


    sinh(x) ≡ [ e^(x) - e^(-x) ] / 2

    cosh(x) ≡ [ e^(x) + e^(-x) ] / 2


    3. The attempt at a solution


    = { [ e^(x) + e^(-x) ] / 2 }² + { [ e^(x) - e^(-x) ] / 2 }²

    = [ e^(x) + e^(-x) ]² / 2² + [ e^(x) - e^(-x) ]² / 2²

    .... gets confusing after this. Thanks in advance.
     
  2. jcsd
  3. Sep 6, 2010 #2

    Mark44

    Staff: Mentor

    How is it confusing? All you are doing is expanding the squares of two binomials. You know how to expand (a + b)2, right?
     
  4. Sep 6, 2010 #3
    Have you tried expanding the brackets on the numerators?
     
  5. Sep 6, 2010 #4
    Not the right attitude ! :)
     
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