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Half-Angle Tangent Identities

\begin{displaymath}
\begin{array}{rclrcl}
\mr {t\;\isdef \;\tan\left(\frac{\theta}{2}\right)}{\frac{\sin(\theta)}{1+\cos(\theta)}}%
{}{\frac{1-\cos(\theta)}{\sin(\theta)}}
\mrone {t^2}{=}{\frac{1-\cos(\theta)}{1+\cos(\theta)}}%
\mr {\sin(\theta)}{\frac{2t}{1+t^2}}%
{\cos(\theta)}{\frac{1-t^2}{1+t^2}}%
\mrone {\tan(\theta)}{=}{\frac{2t}{1-t^2}}
\end{array}\end{displaymath}


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2015-04-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA