Exponential form

1. May 10, 2009

Pietair

1. The problem statement, all variables and given/known data
Prove that:
$$sinh(3x)=3sinh(x)+4sinh^{3}(x)$$

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

and:
$$3sinh(x)=1.5(e^{x}-e^{-x})$$

But I have no idea how to rewrite $$4sinh^{3}(x)$$ in exponential form...

Last edited: May 10, 2009
2. May 10, 2009

phsopher

$$sinh^{3}(x) = [0.5(e^{x}-e^{-x})]^3$$

3. May 10, 2009

Pietair

Allright thanks, then I get:

$$0.5e^{3x}-0.5e^{-3x}=2e^{x}-2e^{-x}$$
Though I have no idea how to continue with this equation...

4. May 10, 2009

phsopher

How exactly did you arrive at that? It works for me.

5. May 10, 2009

Pietair

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

This is not equal to:

$$sinh^{3}(x) = 0.125(e^{3x}-e^{-3x})$$

right?

6. May 10, 2009

phsopher

Remember:

$$(a - b)^3 = a^3 - 3 a^2 b + 3a b^2 - b^3$$

7. May 10, 2009

Pietair

Off course, thanks a lot!