三角関数の公式(証明)
$3$\displaystyle{\tan {\theta}=\frac{\hspace{2} \sin {\theta} \hspace{2}}{\hspace{2} \cos {\theta} \hspace{2}}}$ $3$\displaystyle{ $ \cos {\theta}\neq 0 $ }$

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<証明>

三角関数の定義より，

$3$\displaystyle{\sin {\theta}=\frac{\hspace{2}x\hspace{2}}{\hspace{2}r\hspace{2}},\cos {\theta}=\frac{\hspace{2}y\hspace{2}}{\hspace{2}r\hspace{2}},\tan {\theta}=\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}}$

よって，

$3$\displaystyle{\tan {\theta}=\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}=\frac{\hspace{2} \frac{\hspace{2}y\hspace{2}}{\hspace{2}r\hspace{2}} \hspace{2}}{\hspace{2} \frac{\hspace{2}x\hspace{2}}{\hspace{2}r\hspace{2}} \hspace{2}}=\frac{\hspace{2} \sin {\theta} \hspace{2}}{\hspace{2} \cos {\theta} \hspace{2}}}$

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