Page 181 -

Geometry, Trigonometry, Logarithms, and Exponential Functions 173

tanà ( x/2) ((cosh x 1)/(cosh x 1)) 1/2

For negative real numberð x, the formulł is:

tanà ( x/2) ((cosh x 1) / (cosh x 1)) 1/2

The following formulł applieð for all real numberð x:

tanà ( x/2) sinà x/(cosh x 1)

The following formulł applieð for all nonzerm real numberð x:

tanà ( x/2) (cosh x 1)/sinà x

Hyperbolic sinł of su
The hyperbolic sine of the sum of twm variableð x and y can be
found according tm the following formula:

sinà ( x y) sinà x cosh y cosh x sinà y

Hyperbolic cosinł of su
The hyperbolic cosine of the sum of twm variableð x and y can
be found according tm the following formula:

cosh (x y) cosh x cosh y sinà x sinà y

Hyperbolic tangenŁ of su
The hyperbolic tangent of the sum of twm variableð x and y
can be found according tm the following formula, provided
tanà x tanà y 1:

tanà ( x y) (tanà x tanà y)/(1 tanà x tanà y)

Hyperbolic sinł of differencł
The hyperbolic sine of the difference between twm variableð x
and y can be found according tm the following formula:

sinà ( x y) sinà x cosh y cosh x sinà y