tan ( α ) = sin ( α ) cos ( α ) tan ( α ) = a b sin ( α ) cos ( α ) = a c b c = a c b c = a b ⇓ tan ( α ) = sin ( α ) cos ( α ) {\displaystyle {\begin{aligned}\tan(\alpha )={\frac {\sin(\alpha )}{\cos(\alpha )}}\\\tan(\alpha )={\frac {a}{b}}\\{\frac {\sin(\alpha )}{\cos(\alpha )}}={\frac {\frac {a}{c}}{\frac {b}{c}}}={\frac {ac}{bc}}={\frac {a}{b}}\\\Downarrow \\\tan(\alpha )={\frac {\sin(\alpha )}{\cos(\alpha )}}\\\end{aligned}}}