Osborne's rule

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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.

Subjects: Mathematics.

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