“Osborne’s rule”的概念、定义、翻译、参考文献-科学参考

Osborne’s rule

Mathematics

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 ‘sin’s or ‘sinh’s is involved, where a change of sign is required. For example,

$\begin{array}{l} sin (A + B) = sin A cos B + sin B cos A \\ gives \\ sinh (A + B) = sinh A cosh B + sinh B cosh A, \\ but \\ cos (A + B) = cos A cos B - sin A sin B \\ gives \\ cosh (A + B) = cosh A cosh B + sinh B sinh A . \end{array}$

单词	Osborne’s rule
释义	Osborne’s rule Mathematics 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 ‘sin’s or ‘sinh’s is involved, where a change of sign is required. For example, $\begin{array}{l} sin (A + B) = sin A cos B + sin B cos A \\ gives \\ sinh (A + B) = sinh A cosh B + sinh B cosh A, \\ but \\ cos (A + B) = cos A cos B - sin A sin B \\ gives \\ cosh (A + B) = cosh A cosh B + sinh B sinh A . \end{array}$
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