# 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!
The text contains a mathematical question in the form of a derivation problem and provides a solution to that question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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!
user
The text contains a mathematical question in the form of a derivation problem and provides a solution to that question.

TYPE: SINGLE_QUESTION_WITH_ANSWER