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Sine-Tangent Theorem

If

\begin{displaymath}
{\sin\alpha\over\sin\beta}={m\over n},
\end{displaymath}

then

\begin{displaymath}
{\tan[{\textstyle{1\over 2}}(\alpha-\beta)]\over\tan[{\textstyle{1\over 2}}(\alpha+\beta)]}={m-n\over m+n}.
\end{displaymath}




© 1996-9 Eric W. Weisstein
1999-05-26