 #1
chwala
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 280
 Homework Statement:

Prove the hyperbolic function corresponding to the given trigonometric function.
##8 \sin^4u = 34\cos 2u+\cos 4u##
 Relevant Equations:
 Hyperbolic trig. equations properties.
##8 \sin^4u = 34\cos 2u+\cos 4u##
##8 \sinh^4u = 34(1+2\sinh^2 u)+ \cosh ( 2u+2u)##
##8 \sin^4u = 348\sinh^2 u+ \cosh 2u \cosh 2u + \sinh 2u \sinh 2u##
##8 \sinh^4u = 34+18\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 = 34(1+2\sinh^2 u)+ \cosh ( 2u+2u)##
##8 \sin^4u = 348\sinh^2 u+ \cosh 2u \cosh 2u + \sinh 2u \sinh 2u##
##8 \sinh^4u = 34+18\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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