Derive the identity

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March 21st 2010, 09:19 PM
feronius

Derive the identity

hey just having a little trouble with this problem,

Derive the identity:
sinh x cosh y = (1/2)[sinh(x+y)+sinh(x-y)]

thanks!
March 21st 2010, 10:51 PM
matheagle

Just substitute the definitions and multiply.

$(1/2)[\sinh(x+y)+\sinh(x-y)]=(1/4)\left[ e^{x+y}-e^{-x-y}+e^{x-y}-e^{-x+y}\right]$

likewise....

$\sinh x \cosh y= \left({e^x-e^{-x}\over 2}\right)\left({e^y+e^{-y}\over 2}\right)$
March 23rd 2010, 07:01 PM
feronius

thanks, didnt realise it was as simple as that, muchly appreciated!

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