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\begin{document}
\twocolumn[\hfill{\Large \bf �s�֐��t���@�藝} 
\hfill\hfill\hfill
$�N���X\underline{\kern3zw}\kern1zw �ԍ�\underline{\kern3zw}\kern1zw
����\underline{\kern14zw}$\vspace{.5em}]\medskip

\subsection*{�����@�藝}
$\sin(\alpha+\beta)=\sin\alpha+\sin\beta$�͐������Ȃ�. 
���Ƃ���, $\alpha=30\Deg,~\beta=60\Deg$�̂Ƃ�, 
$\alpha+\beta=90\Deg$���, 
$\sin(\alpha+\beta)=\sin90\Deg=1$�ł��邪, 
$\sin\alpha+\sin\beta=\sin30\Deg+\sin60\Deg=\bunsuu12+\bunsuu{\sqrt{3}}{2}$
�ł���. 

�ȉ��ł�, 
$\sin(\alpha+\beta)$��$\alpha, \beta$�̃T�C��, �R�T�C���̊Ԃ�
�ǂ̂悤�Ȋ֌W�����邩���l����. 

\medskip
\begin{Fmawarikomi}{.15\textwidth}
{\quad
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	% �ȏ��, emath�̌Â��o�[�W�����ł̏������ɂȂ�
	% \tenretu �𗘗p�����,
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�E�}�ł�, $\alpha,\beta, \alpha+\beta$�����������1�ی��̊p�Ƃ���. 
FD��OX�͕��s�Ȃ̂�, $\kaku{AOX}=\kaku{ODF}=\alpha$�ł���. 
���̂Ƃ�, 
$\sankaku{BDG}\souzi \sankaku{DFG}$�ł��邩��, 
	% �����̋L����, emath �𗘗p���邵���Ȃ��I
	% amsmath �ɂ�, ���̋L���͒�`����Ă��Ȃ�. 
$\kaku{DBG}=\kaku{FDG}=\alpha$�ƂȂ�̂�, 
$\sankaku{BOC}$��, 
	% �p�L����O�p�`�̋L����amsmath�ɂ�����܂�. ��r���Ă݂Ă�������.
$\sin(\alpha+\beta)=\bunsuu{\rm OB}{\rm BC}={\rm BC}
={\rm BF}+{\rm FC}={\rm BF}+{\rm DE}$�ł���. \\
BF��DE��, ���̂��Ƃ��狁�߂���. \\
�܂�, $\sankaku{BOD}$�ɂ�����, 
$\sin\beta=\bunsuu{\rm BD}{\rm OB}={\rm BD}$�ł���. \\
���, $\sankaku{BDF}$�ɂ�����, 
$\cos\alpha=\bunsuu{\rm BF}{\rm BD}$�Ȃ̂�, 
${\rm BF}={\rm BD}\cos\alpha=\cos\alpha\sin\beta$�ł���. \\
����, $\sankaku{DOE}$�ɂ�����, 
$\sin\alpha=\bunsuu{\rm DE}{\rm OD}$���, 
${\rm DE}={\rm OD}\sin\alpha$�ł���. \\
$\sankaku{BOD}$�ɂ�����, 
$\cos\beta=\bunsuu{\rm OD}{\rm OB}={\rm OD}$�ł��邩��, 
${\rm DE}=\sin\alpha\cos\beta$�ł���. 
�ȏ���, \\
\[\sin(\alpha+\beta)={\rm BF}+{\rm DE}
=\sin\alpha\cos\beta+\cos\alpha\sin\beta\]
�ƂȂ�. 
\end{Fmawarikomi}

�����,  $\sin(-\theta)=-\sin\theta, \cos(-\theta)=\cos\theta$�ł��邩��, 
$\sin(\alpha-\beta)$�̏ꍇ�ɂ͎����̂悤�ɂȂ�. 
\[\sin(\alpha-\beta)=\sin(\alpha+(-\beta))
=\sin\alpha\cos(-\beta)+\cos\alpha\sin(-\beta)
=\sin\alpha\cos\beta-\cos\alpha\sin\beta\]

\medskip
���l�ɂ����, 
$\begin{aligned}[t]
cos(\alpha+\beta)&=\bunsuu{\rm OC}{\rm OB}={\rm OC}
={\rm OE}-{\rm CE}={\rm OE}-{\rm FD}\\
&={\rm OD}\cos\alpha-{\rm BD}\sin\alpha
=\cos\alpha\cos\beta-\sin\alpha\sin\beta
\end{aligned}$\\
�ƂȂ�. �܂�, $\alpha,\beta$�̃T�C��, �R�T�C���̒l���������, 
$\alpha+\beta$�̃T�C��, �R�T�C���̒l�����߂���.  

����ɂ�, $\tan\theta=\bunsuu{\sin\theta}{\cos\theta}$�ł��邩��, 
���L�̎��̕��q�ƕ����$\cos\alpha\cos\beta$�Ŋ��邱�Ƃɂ��, 
\[
\tan(\alpha+\beta)
=\bunsuu{\sin(\alpha+\beta)}{\cos(\alpha+\beta)}
=\bunsuu{\sin\alpha\cos\beta+\cos\alpha\sin\beta}
{\cos\alpha\cos\beta-\sin\alpha\sin\beta}
=\bunsuu{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}
\]
���ȏ�̊֌W��, $\alpha, \beta, \alpha+\beta$����1�ی��ɂȂ�
�ꍇ�ł���������. 
\begin{itemshadebox}[r]{\bf ���@�藝}
\renewcommand{\labelenumi}{(\arabic{enumi})}
\begin{enumerate}
\item $\mbf{\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta}$
\item $\mbf{\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta}$
\item $\mbf{\tan(\alpha\pm\beta)=\bunsuu{\tan\alpha\pm\tan\beta}{1\mp\tan\alpha\tan\beta}}$
\end{enumerate}
\end{itemshadebox}

\rei
$\sin105\Deg=\sin(60\Deg+45\Deg)=\sin60\Deg\cos45\Deg+\cos60\Deg\cos45\Deg
=\bunsuu{\sqrt{3}}{2}\bunsuu{\sqrt{2}}{2}
+\bunsuu{1}{2}\bunsuu{\sqrt{2}}{2}
=\bunsuu{\sqrt{6}+\sqrt{2}}{4}$

\rei
$\tan105\Deg=\tan(45\Deg+60\Deg)
=\bunsuu{\tan45\Deg+\tan60\Deg}{1-\tan45\Deg\tan60\Deg}$\\
\hspace*{7em}$=\bunsuu{1+\sqrt{3}}{1-\sqrt{3}}=\bunsuu{(1+\sqrt{3})^2}{1-3}
=\bunsuu{4+2\sqrt{3}}{-2}=-2-\sqrt{3}$

\newpage
\rei �p$\alpha$�͑�2�ی��̊p��$\sin\alpha=\bunsuu35$, 
�p$\beta$�͑�3�ی��̊p��$\cos\beta=-\bunsuu{5}{13}$�Ƃ���Ƃ�, 
$\sin(\alpha-\beta)$�̒l�����߂�. 

\kai
\qquad $\cos\alpha=-\bunsuu45,~\sin\beta=-\bunsuu{12}{13}$�Ȃ̂�, 
\[
\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta
=\bunsuu35\cdot\left(-\bunsuu5{13}\right)
-\left(-\bunsuu45\right)\cdot\left(-\bunsuu{12}{13}\right)
=-\bunsuu{63}{65}
\]

\begin{enumerate}
\item ���@�藝��p����, �����̒l�����߂�. 
\begin{edaenumerate}
\item $\sin75\Deg$
\item $\cos75\Deg$
\vfill
\item $\tan75\Deg$
\item $\sin15\Deg$
\vfill
\item $\cos15\Deg$
\item $\tan15\Deg$
\vfill
\end{edaenumerate}

\newpage
\item �p$\alpha$����1�ی��̊p��$\sin\alpha=\bunsuu12$, 
�p$\beta$�͑�3�ی��̊p��$\cos\beta=-\bunsuu45$�̂Ƃ�, 
$\tan(\alpha+\beta)$�̒l�����߂�. 
\vfill

\item $\sin\theta=\bunsuu13~(0<\theta<\bunsuu{\pi}{2})$�̂Ƃ�, 
$\cos\left(\theta-\bunsuu{\pi}{3}\right)$�̒l�����߂�. 
\vfill

\item �p$\alpha$�͑�2�ی��̊p��$\sin\alpha=\bunsuu23$�̂Ƃ�, 
�����̒l�����߂�. 
\begin{edaenumerate}
\item $\cos\alpha$
\item $\tan\alpha$
\vfill

\newpage
% �ȉ���, ���p�Ƃ��ďo�肵�����̂ł�. 
% ���̎��_��, 2�{�p��3�{�p�̌����͐������Ă��܂���.
\item $\sin2\alpha$
\item $\cos2\alpha$
\vfill
\item $\sin3\alpha$
\item $\cos4\alpha$
\vfill\vfill
\end{edaenumerate}
\end{enumerate}

\end{document}

