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

##8 \sin^4u = 3-4\cos 2u+\cos 4u##

- Relevant Equations
- Hyperbolic trig. equations properties.

##8 \sin^4u = 3-4\cos 2u+\cos 4u##

##8 \sinh^4u = 3-4(1+2\sinh^2 u)+ \cosh ( 2u+2u)##

##8 \sin^4u = 3-4-8\sinh^2 u+ \cosh 2u \cosh 2u + \sinh 2u \sinh 2u##

##8 \sinh^4u = 3-4+1-8\sinh^2 u+ 4\sinh^2u +4\sinh^4 u + 4\sinh^2 u + 4\sinh^4 u##

##8 \sinh^4u = -8\sinh^2 u+ 8\sinh^2u +8\sinh^4 u##

##8 \sinh^4u=8\sinh^4 u##

Thus proved that lhs = rhs

Insight welcome...nothing much here...

##8 \sinh^4u = 3-4(1+2\sinh^2 u)+ \cosh ( 2u+2u)##

##8 \sin^4u = 3-4-8\sinh^2 u+ \cosh 2u \cosh 2u + \sinh 2u \sinh 2u##

##8 \sinh^4u = 3-4+1-8\sinh^2 u+ 4\sinh^2u +4\sinh^4 u + 4\sinh^2 u + 4\sinh^4 u##

##8 \sinh^4u = -8\sinh^2 u+ 8\sinh^2u +8\sinh^4 u##

##8 \sinh^4u=8\sinh^4 u##

Thus proved that lhs = rhs

Insight welcome...nothing much here...

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