Sin 75 + sin 15 per cos 105 - cos 15

[tex] \frac{ \sin(75) + \sin(15) }{ \cos(105) - \cos(15) } \\ = \frac{2 \sin( \frac{ \alpha + \beta }{2}) \cos( \frac{ \alpha - \beta }{2} ) }{ - 2 \sin( \frac{ \alpha + \beta }{2} ) \sin( \frac{ \alpha - \beta }{2} ) } \\ = \frac{2 \sin( \frac{75 + 15}{2} ) \cos( \frac{75 - 15}{2} ) }{ - 2 \sin( \frac{105 + 15}{2} ) \sin( \frac{105 - 15}{2}) } \\ = \frac{2 \sin(45) \cos(30) }{ - 2 \sin(60) \sin(45) } \\ = \frac{2( \frac{1}{2} \sqrt{2} )( \frac{1}{2} \sqrt{3}) }{ - 2( \frac{1}{2} \sqrt{3})( \frac{1}{2} \sqrt{2} ) } \\ = - 1[/tex]
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