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April 18, 2014

April 18, 2014

Posted by **jh** on Monday, March 22, 2010 at 4:05am.

Show that

(cosh x)^2 - (sinh x)^2 = 1

for every real number x.

- Precalculus -
**MathMate**, Monday, March 22, 2010 at 8:24amExpand and simplify using:

cosh(x)=(e^{x}+e^{-x})/2

sinh(x)=(e^{x}-e^{-x})/2

noting that e^{x}* e^{-x}=1

For the domain, since both e^{x}and e^{-x}have a domain of R, so the expression cosh(x)²-sinh(x)²=1

also has a domain of R, or (-∞,&infin).

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