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Proving hyperbolic trig formula

  1. Sep 2, 2005 #1
    hello everyone..could you please help me with these 2:

    cosh^2 X=(cosh (2X)+1)/2

    sinh(X+Y)=sinh X.cosh Y+cosh X.sinh Y
     
  2. jcsd
  3. Sep 2, 2005 #2
    How about using the definitions of cosh and sinh in terms of exponentials and use some standard rules for exponents? Show your work!
     
  4. Sep 2, 2005 #3

    Curious3141

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    Even easier : what relationships do you know between the usual trigonometric functions of imaginary variables and the hyperbolic trig functions of those variables ? The problem can be reduced to simple compond angle trig.
     
  5. Sep 2, 2005 #4
    Here it is for circular trig. functions:

    [tex]\cos{2x}=\cos^2{x}-\sin^2{x}=2\cos^2{x}-1[/tex]

    From here, you can solve for [itex]\cos^2{x}[/itex] and you will have your answer for circular functions. Now, apply this to hyperbolic functions.
     
  6. Sep 3, 2005 #5
    thanks

    thanks for your help...
     
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