The Addition Formulas

The following formulas are of the most essential trigonometric formulas that will be utilized in the subsequent text, their proof is attached by the end of this section:

$\cos{(\phi \pm \alpha)} = \cos{(\phi) \cdot \cos{(\alpha)}} \mp \sin{(\phi)} \cdot \sin{(\alpha)}$ «1»
$\sin{(\phi \pm \alpha)} = \sin{(\phi)} \cdot \cos{(\alpha)} \pm \cos{(\phi)} \cdot \sin{(\alpha)}$ «2»
$\tan{(\phi \pm \alpha)} = \frac{\tan{\phi} \pm \tan{\alpha}}{1 \mp \tan{\phi} \cdot \tan{\alpha}}$ «3»

$\begin{tcolorbox} % latex2html id marker 573 [colback=black!10!white, colframe=b... ...\cdot\sin{\alpha} \end{displaymath} \end{tcolorbox} \medskip\par\end{tcolorbox}$

$\begin{tcolorbox} % latex2html id marker 729 [colback=black!10!white, colframe=b... ...phi}\cdot\sin{\alpha} \end{displaymath} \end{tcolorbox} \medskip\end{tcolorbox}$

$\begin{tcolorbox} % latex2html id marker 771 [colback=black!10!white, colframe=b... ...cdot\tan{\phi} } \end{displaymath} \end{tcolorbox} \medskip\par\end{tcolorbox}$

$\begin{tcolorbox} % latex2html id marker 843 [colback=black!10!white, colframe=b... ...pi)} \\ = - \cos(\phi) \) \end{proof} \end{tcolorbox} \medskip\end{tcolorbox}$