text: # Derive the identity
  
  • Mar 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!
  • Mar 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....
  
  $\sinh x \cosh y= \left({e^x-e^{-x}\over 2}\right)\left({e^y+e^{-y}\over 2}\right)$
  • Mar 23rd 2010, 07:01 PM
  feronius
  thanks, didnt realise it was as simple as that, muchly appreciated!
explanation: The document is a forum post where a user named feronius asks for help in deriving a specific hyperbolic identity. Another user, matheagle, provides a step-by-step solution to the problem. The original poster then thanks matheagle for the help.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Derive the identity
  
  • Mar 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!
  • Mar 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....
  
  $\sinh x \cosh y= \left({e^x-e^{-x}\over 2}\right)\left({e^y+e^{-y}\over 2}\right)$
  • Mar 23rd 2010, 07:01 PM
  feronius
  thanks, didnt realise it was as simple as that, muchly appreciated!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum post where a user named feronius asks for help in deriving a specific hyperbolic identity. Another user, matheagle, provides a step-by-step solution to the problem. The original poster then thanks matheagle for the help.
  
  Label: question-and-answer