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Function Product Identities


                                                       1              1
                                          sin x sin y =  cos(x − y) −   cos(x + y)
                                                       2              2
                                                       1               1
                                          cos x cos y =  cos(x − y) +   cos(x + y)
                                                       2               2
                                                       1              1
                                          sin x cos y =  sin(x + y) +   sin(x − y)
                                                       2              2
                                                       1              1
                                          cos x sin y =  sin(x + y) −   sin(x − y)
                                                       2              2

                   Exponential Identities

                                                                                       ix
                                                               ix
                                                              e − e  −ix              e + e −ix
                              ix
                             e = cos x + i sin x,     sin x =           ,     cos x =
                                                                  i2                      2
                   G.2       Hyperbolic Functions

                   Exponential Identities

                                                    x
                                                                            x
                                                   e − e −x                e + e −x
                                          sinh x =         ,     cosh x =
                                                      2                       2
                                                                     x
                                                          sinh x    e − e −x
                                                tanh x =         =
                                                                     x
                                                          cosh x    e + e −x
                   Reciprocal Identities
                                            1                     1                     1
                                 csch x =       ,     sech x =        ,    coth x =
                                          sinh x               cosh x                tanh x

                   Pythagorean Identities
                                                                      2
                                                    2
                                          2
                                                                               2
                                      cosh x − sinh x = 1,       tanh x + sech x = 1
                   Relation to Circular Functions



                                         sinh(ix) = i sin x     sinh x = −i sin(ix)
                                         cosh(ix) = cos x       cosh x = cos(ix)
                                         tanh(ix) = i tan x     tanh x = −i tan(ix)














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