Proving hyperbolic trig formula

  • Thread starter tuly
  • Start date
  • #1
tuly
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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
 

Answers and Replies

  • #2
da_willem
599
1
How about using the definitions of cosh and sinh in terms of exponentials and use some standard rules for exponents? Show your work!
 
  • #3
Curious3141
Homework Helper
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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.
 
  • #4
amcavoy
665
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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.
 
  • #5
tuly
4
0
thanks

thanks for your help...
 

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