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

Can anyone help me with this question please!!

Show that

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

for every real number x.

- Precalculus -
**MathMate**, Monday, March 22, 2010 at 8:24am
Expand 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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