sinh(a ± b) = sinh a cosh b ± cosh a sinh b

cosh(a ± b) = cosh a cosh b ± sinh a sinh b

                        tanh a ± tanh b

tanh(a ± b) = ـــــــــــــــــــــــــــــــــــــــ

                       1 ± tanh a tanh b

e^x = sinh(x) + cosh(x)

e^–x = cosh(x) – sinh(x)

cosh²(x) – sinh²(x) = 1

sech²(x) + tanh²(x) = 1

coth²(x) – csch²(x) = 1

                      2tanh(x)

tanh(2x) = ـــــــــــــــــــــــــــــ

                    1 ± tanh²x

cosh²(x) = ½(cosh(2x) + 1)

sinh²(x) = ½(cosh(2x) – 1)

sinh(2x) = 2 sinh(x) cosh(x) 

cosh(2x) = sinh²x + cosh²x   OR

cosh(2x) = 2sinh²x + 1          OR

cosh(2x) = 2cosh²x – 1

sinh(–x)  = – sinh(x)

cosh(–x)  = cosh(x)

tanh(–x)  = – tanh(x)

sinh a cosh b = ½[sinh(a + b) + sinh(a – b)]

cosh a sinh b = ½[sinh(a + b) – sinh(a – b)]

cosh a cosh b = ½[cosh(a + b) + cosh(a – b)]

sinh a sinh b = ½[cosh(a + b) – cosh(a – b)]

tansh x = sinh x : cosh x

sech x = 1 : sinh x

csch x = 1 : cosh x

coth x = 1 : tanh x

sinh a + sinh b =2sinh½(a+b)cosh½(a–b)

sinh a – sinh b =2cosh½(a+b)sinh½(a–b)

cosh a + cosh b =2cosh½(a+b)cosh½(a–b)

cosh a – sinh b =2sinh½(a+b)sinh½(a–b)