Can anyone help me with this question please!!

Question

Show that
(cosh x)^2 - (sinh x)^2 = 1
for every real number x.

Answer 1

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).