Asked by jh
Can anyone help me with this question please!!
Show that
(cosh x)^2 - (sinh x)^2 = 1
for every real number x.
Show that
(cosh x)^2 - (sinh x)^2 = 1
for every real number x.
Answers
Answered by
MathMate
Expand and simplify using:
cosh(x)=(e<sup>x</sup>+e<sup>-x</sup>)/2
sinh(x)=(e<sup>x</sup>-e<sup>-x</sup>)/2
noting that e<sup>x</sup> * e<sup>-x</sup>=1
For the domain, since both e<sup>x</sup> and e<sup>-x</sup> have a domain of R, so the expression cosh(x)²-sinh(x)²=1
also has a domain of R, or (-∞,&infin).
cosh(x)=(e<sup>x</sup>+e<sup>-x</sup>)/2
sinh(x)=(e<sup>x</sup>-e<sup>-x</sup>)/2
noting that e<sup>x</sup> * e<sup>-x</sup>=1
For the domain, since both e<sup>x</sup> and e<sup>-x</sup> 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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