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trigsubs

handle trigonometric identities

 Calling Sequence trigsubs(expr) trigsubs(s) trigsubs(s, expr)

Parameters

 expr - expression s - equation

Description

 • The function trigsubs manages a table of valid trigonometric identities.
 • If trigsubs is called with the single argument $0$, it returns a set of functions known to the procedure.
 • If trigsubs is called with a single trigonometric expression expr, it returns a list of trigonometric expressions equal to expr.
 • If trigsubs is called with a single equation s which represents a trigonometric identity, it returns found if this identity belongs to the table, and not found otherwise.
 • If trigsubs is called with two arguments, it checks whether the identity s belongs to the table or not.  In the former case, the function applies this identity to expr and returns the result.  In the latter case, the function returns an error message.
 • For substitution of identities not known to this procedure, use subs.

Examples

 > $\mathrm{trigsubs}\left(0\right)$
 $\left\{{\mathrm{cos}}{,}{\mathrm{cosh}}{,}{\mathrm{cot}}{,}{\mathrm{coth}}{,}{\mathrm{csc}}{,}{\mathrm{csch}}{,}{\mathrm{exp}}{,}{\mathrm{sec}}{,}{\mathrm{sech}}{,}{\mathrm{sin}}{,}{\mathrm{sinh}}{,}{\mathrm{tan}}{,}{\mathrm{tanh}}\right\}$ (1)
 > $\mathrm{trigsubs}\left(\mathrm{cos}\left(a+bw\right)\right)$
 $\left[{\mathrm{cos}}{}\left({-}{b}{}{w}{-}{a}\right){,}{{\mathrm{cos}}{}\left(\frac{{1}}{{2}}{}{b}{}{w}{+}\frac{{1}}{{2}}{}{a}\right)}^{{2}}{-}{{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}{b}{}{w}{+}\frac{{1}}{{2}}{}{a}\right)}^{{2}}{,}\frac{{1}}{{\mathrm{sec}}{}\left({b}{}{w}{+}{a}\right)}{,}\frac{{1}{-}{{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{b}{}{w}{+}\frac{{1}}{{2}}{}{a}\right)}^{{2}}}{{1}{+}{{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{b}{}{w}{+}\frac{{1}}{{2}}{}{a}\right)}^{{2}}}{,}\frac{{1}}{{2}}{}{{ⅇ}}^{{I}{}\left({b}{}{w}{+}{a}\right)}{+}\frac{{1}}{{2}}{}{{ⅇ}}^{{-}{I}{}\left({b}{}{w}{+}{a}\right)}{,}{\mathrm{cos}}{}\left({b}{}{w}\right){}{\mathrm{cos}}{}\left({a}\right){-}{\mathrm{sin}}{}\left({b}{}{w}\right){}{\mathrm{sin}}{}\left({a}\right)\right]$ (2)
 > $\mathrm{trigsubs}\left(\mathrm{cos}\left(w\right)=\mathrm{sin}\left(w\right)\right)$
 ${\mathrm{not found}}$ (3)
 > $\mathrm{trigsubs}\left(\mathrm{cos}\left(w\right)=\mathrm{sin}\left(w\right),1\right)$
 > $\mathrm{trigsubs}\left(\mathrm{sin}\left(2z\right)=2\mathrm{cos}\left(z\right)\mathrm{sin}\left(z\right),\mathrm{sin}\left(2z\right)\mathrm{cos}\left(z\right)\right)$
 ${2}{}{{\mathrm{cos}}{}\left({z}\right)}^{{2}}{}{\mathrm{sin}}{}\left({z}\right)$ (4)