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%This command provides the additional trigonometric functions
%displayed in the column three of the page 4
%
%The command has one parameter:
% 1) The width of the text
\newcommand\TFourTrigTwo[1]{%
\parbox[t]{#1}{%
\deflength\TmpLengthA{3ex plus .5ex minus 1.5ex}
\DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace}
%Since the width of the column is narrow, ragged right
%looks better
\raggedright
\input{triangle.tex}
\usebox\TriangleBox
\TFourTitle{Law of cosines:}
\begin{DisplayFormulae}{1}{0pt}{\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
\def\FirstPart{c^2 = \mbox{}}
\FmPartA{\FirstPart a^2 + b^2 -}.
\FmPartB{\FirstPart}{2ab \cos C}.
\end{DisplayFormulae}
\TFourTitle{Area:}
\AdjustSpace{-2.5ex plus .5ex minus .5ex}
\begin{DisplayFormulae}{1}{0pt}{1.1\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
\def\FirstPart{A}
\FmPartA{\FirstPart = \tfrac{1}{2} h c = \tfrac{1}{2} a b \sin C}
\FmPartB{\FirstPart}{= \tfrac{c^2 \sin A \sin B}{2 \sin C}}
\end{DisplayFormulae}
\TFourTitle{Heron's formula:}
\begin{DisplayFormulae}{1}{0pt}{.9\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
\Fm{A = \sqrt{s \cdot s_a \cdot s_b \cdot s_c}}
\Fm{s = \tfrac{1}{2} (a + b + c)}
\Fm{s_a = s - a}
\Fm{s_b = s - b}
\Fm{s_c = s - c}
\end{DisplayFormulae}
\TFourTitle{More identities:}
\begin{DisplayFormulae}{1}{0pt}{\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
\def\FmSep{\unskip\text{,}}%Comma is the separator of equation
\Fm{\sin \tfrac{x}{2} = \sqrt{\dfrac{1 - \cos x}{2}}}
\Fm{\cos \tfrac{x}{2} = \sqrt{\dfrac{1 + \cos x}{2}}}
\def\FirstPart{\tan \tfrac{x}{2}}%
\FmPartA{\FirstPart = \sqrt{\dfrac{1 - \cos x}{1 + \cos x}}}
\FmPartB{\FirstPart}{\!= \dfrac{1 - \cos x}{\sin x}}
\FmPartB{\FirstPart}{\!= \dfrac{\sin x}{1 + \cos x}}
\def\FirstPart{\cot \tfrac{x}{2}}
\FmPartA{\FirstPart = \sqrt{\dfrac{1 + \cos x}{1 - \cos x}}}
\FmPartB{\FirstPart}{\!=\dfrac{1 + \cos x}{\sin x}}
\FmPartB{\FirstPart}{\!=\dfrac{\sin x}{1 - \cos x}}
\Fm{\sin x = \dfrac{e^{ix} - e^{-ix}}{2 i}}
\Fm{\cos x = \dfrac{e^{ix} + e^{-ix}}{2}}
\def\FirstPart{\tan x}
\FmPartA{\FirstPart = -i \dfrac{e^{ix} - e^{-ix}}{e^{ix} + e^{-ix}}}
\FmPartB{\FirstPart}{\!=-i \dfrac{e^{2ix} - 1}{e^{2ix} + 1}}
\Fm{\sin x = \dfrac{\sinh i x}{i}}
\Fm{\cos x = \cosh i x}
\def\FmSep{\unskip\text{.}}
\Fm{\tan x = \dfrac{\tanh i x}{i}}
\end{DisplayFormulae}
}%
}
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