- #1

chwala

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- Homework Statement
- Prove the hyperbolic function corresponding to the given trigonometric function.

##\sin 3x = 3\sin x- 4\sin^3x##

- Relevant Equations
- hyperbolic trig. properties.

We shall have;

##\sinh 3x = 3\sinh x- 4\sinh^3x##

##\sinh 3x =\sinh (2x+x)=\sinh 2x \cosh x + \cosh 2x \sinh x##

##\sinh 3x= 2\sinh x \cosh x \cosh x + (1+2 \sin^2x) \sinh x##

##\sinh 3x=2 \sinh x \cosh^2 x + \sinh x + 2\sinh^3x##

##\sinh 3x= 2\sinh x + 2\sinh^3 x + \sinh x + 2\sinh^3x##

##\sinh 3x = 4\sinh^3x + 3 \sinh x##

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##\sinh 3x = 3\sinh x- 4\sinh^3x##

##\sinh 3x =\sinh (2x+x)=\sinh 2x \cosh x + \cosh 2x \sinh x##

##\sinh 3x= 2\sinh x \cosh x \cosh x + (1+2 \sin^2x) \sinh x##

##\sinh 3x=2 \sinh x \cosh^2 x + \sinh x + 2\sinh^3x##

##\sinh 3x= 2\sinh x + 2\sinh^3 x + \sinh x + 2\sinh^3x##

##\sinh 3x = 4\sinh^3x + 3 \sinh x##

Insight welcome...today i have been singing shine shine shine