Buktikan bahwa Sec α - cos α = sin α tan α

[tex] \sec( \alpha ) - \cos( \alpha ) = \frac{1}{ \cos( \alpha ) } - \cos( \alpha ) \\ = \frac{1}{ \cos( \alpha ) } - \frac{ { \cos}^{2}( \alpha ) }{ \cos( \alpha ) } \\ = \frac{1 - { \cos}^{2} ( \alpha )}{ \cos( \alpha ) } \\ = \frac{ { \sin}^{2} ( \alpha )}{ \cos( \alpha ) } \\ = \sin( \alpha ) . \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ = \sin( \alpha ) \tan( \alpha ) [/tex]
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