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Angle Sum and Difference Identities



                                   sinh(x ± y) = sinh x cosh y ± cosh x sinh y
                                   cosh(x ± y) = cosh x cosh y ± sinh x sinh y
                                                    tanh x ± tanh y     sinh 2x ± sinh 2y
                                   tanh(x ± y) =                     =
                                                   1 ± tanh x tanh y    cosh 2x ± cosh 2y
                                                   1 ± coth x coth y   sinh 2x ∓ sinh 2y
                                   coth(x ± y) =                    =
                                                   coth x ± coth y     cosh 2x − cosh 2y


                   Function Sum and Difference Identities

                                                               1             1
                                       sinh x ± sinh y = 2 sinh (x ± y) cosh (x ∓ y)
                                                               2             2
                                                               1              1
                                       cosh x + cosh y = 2 cosh (x + y) cosh (x − y)
                                                               2              2
                                                               1             1
                                       cosh x − cosh y = 2 sinh (x + y) sinh (x − y)
                                                               2             2
                                                          sinh(x ± y)
                                       tanh x ± tanh y =
                                                          cosh x cosh y
                                                         sinh(x ± y)
                                       coth x ± coth y =
                                                         sinh x sinh y




                   Double Angle Identities

                                                                                        2
                                                                              2
                                  sinh 2x = 2 sinh x cosh x,    cosh 2x = cosh x + sinh x
                   Half Angle Identities

                                            x    cosh x − 1            x    cosh x + 1
                                      sinh 2  =            ,     cosh 2  =
                                            2        2                 2        2


                   Function Product Identities

                                                       1               1
                                       sinh x sinh y =   cosh(x + y) −   cosh(x − y)
                                                       2               2
                                                       1                1
                                       cosh x cosh y =   cosh(x + y) +    cosh(x − y)
                                                       2                2
                                                       1               1
                                       sinh x cosh y =   sinh(x + y) +   sinh(x − y)
                                                       2               2










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