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Appendix

This document contains several hyperbolic identities involving trigonometric hyperbolic functions such as sinh, cosh, tanh, coth, sech, and csch. It lists quotient identities that relate tanh and coth to sinh and cosh, reciprocal identities that relate the reciprocals of these functions to one another, and fundamental identities involving expressions of sinh, cosh, tanh, coth, and their squares.

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Gladys Perez
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34 views2 pages

Appendix

This document contains several hyperbolic identities involving trigonometric hyperbolic functions such as sinh, cosh, tanh, coth, sech, and csch. It lists quotient identities that relate tanh and coth to sinh and cosh, reciprocal identities that relate the reciprocals of these functions to one another, and fundamental identities involving expressions of sinh, cosh, tanh, coth, and their squares.

Uploaded by

Gladys Perez
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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APPENDIX

HYPERBOLIC IDENTITIES

Quotient Identities

sinh u
tanh u 
cosh u

cosh u
coth u 
sinh u

Reciprocal Identities

1 1 1
tanh u  cosh u  sinh u 
coth u sec hu csch u
1 1 1
coth u  sec hu  csch u 
tanh u cosh u sinh u

Fundamental Identities

cosh 2 u  sinh 2 u  1
1  tanh 2 u  sech 2 u
1  coth 2 u   csch 2 u
sinh 2u  2sinh u cosh u
cosh 2u  cosh 2 u  sinh 2 u

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