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Posted by 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 - , Monday, March 22, 2010 at 8:24am

    Expand and simplify using:
    cosh(x)=(ex+e-x)/2
    sinh(x)=(ex-e-x)/2
    noting that ex * e-x=1

    For the domain, since both ex 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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