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Exponential form

  • Thread starter Pietair
  • Start date
  • #1
59
0

Homework Statement


Prove that:
[tex]sinh(3x)=3sinh(x)+4sinh^{3}(x)[/tex]

2. The attempt at a solution
I know that:
[tex]sinh(3x)=0.5(e^{3x}-e^{-3x})[/tex]

and:
[tex]3sinh(x)=1.5(e^{x}-e^{-x})[/tex]

But I have no idea how to rewrite [tex]4sinh^{3}(x)[/tex] in exponential form...
 
Last edited:

Answers and Replies

  • #2
180
4
[tex]sinh^{3}(x) = [0.5(e^{x}-e^{-x})]^3[/tex]
 
  • #3
59
0
Allright thanks, then I get:

[tex]0.5e^{3x}-0.5e^{-3x}=2e^{x}-2e^{-x}[/tex]
Though I have no idea how to continue with this equation...
 
  • #4
180
4
How exactly did you arrive at that? It works for me.
 
  • #5
59
0
I made a mistake.

[tex]sinh^{3}(x) = 0.125[(e^{x}-e^{-x})]^3[/tex]

This is not equal to:

[tex]sinh^{3}(x) = 0.125(e^{3x}-e^{-3x})[/tex]

right?
 
  • #6
180
4
Remember:

[tex] (a - b)^3 = a^3 - 3 a^2 b + 3a b^2 - b^3[/tex]
 
  • #7
59
0
Off course, thanks a lot!
 

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