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Trigonometric Identities, Continued

\begin{eqnarray*}
\mr {\sin(A)-\sin(B)}{2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)}%
{\cos(A)-\cos(B)}{-2\sin\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)}
\mr {\sin^2(A)-\sin^2(B)}{\sin(A+B)\sin(A-B)}%
{\cos^2(A)-\cos^2(B)}{-\sin(A+B)\sin(A-B)}
\mrone {\cos^2(A)-\sin^2(B)}{=}{\cos(A+B)\cos(A-B)}
\mrone {\tan(\theta)}{\isdef }{\frac{\sin(\theta)}{\cos(\theta)}}
\mr {\tan(A)+\tan(B)}{\frac{\sin(A+B)}{\cos(A)\cos(B)}}%
{\tan(A+B)}{\frac{\tan(A+B)}{1-\tan(A)\tan(B)}}
\end{eqnarray*}


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2015-03-04 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA