The rule which summarizes the correspondence between trigonometric and hyperbolic function identities. It states that the identities are the same except where a product of two sins or sinhs is involved, where an extra negative is required. For example,
sin (A+B)=sin A cos B+sin B cos A gives
sinh(A+B)=sinh A cosh B+sinh B cosh A, but
cos(A+B)=cos A cos B−sin A sin B gives
cosh(A+B)=cosh A cosh B−sinh B sinh A.