I need help with proving osborn's rule.
#Proof for Osborn's Rule
hollow hornet
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I need help with proving osborn's rule.
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hollow hornet
"Osborn's rule is a rule for converting a trigonometric identity into a corresponding hyperbolic one. The rule states that one replaces every occurrence of sine or cosine with the corresponding hyperbolic sine or cosine, and wherever one has a product of two sines, the product of the hyperbolic sines must be negated."
i 100% get how it works
but what is the proof? how did George Osborn derive it?
it's a neat trick but how it is proven is beyond me
hollow hornet
umm
i guess so?
it works for tan's aswell, but thats because you can break it down into sin/cos
so i would imagine
and the rule holds true for all x
to my knowledge
final spire
if you map x->ix, then sin->isinh, cos->cosh
i am kinda right
hollow hornet
alr lets see
final spire
https://math.stackexchange.com/questions/138842/proof-of-osborns-rule
!!! they proved osborne's rule not osborn's rule
invalidated
final spire
do you know about the $\frac{e^{ix} + e^{-ix}}{2}$ definitions
vivid wingBOT
cute rizzler bear?
lusty viper
yes yes i know these
sin ix = isinh x and cos ix = cosh x
right ?
I haven't learnt hyperbolic functions properly yet so I will need to know if what I know is true or not ☠️
lusty viper
sin ix = isinh x and cos ix = cosh x
right ?
but if this is true, we will and we take identity, sin^2x gets replaced with -sinh^2 x because of i*i 
or in sinasinb, -(sinh a)(sinh b)