sin 75° + sin 15° / cos 105° - cos 15° =

[tex] \frac{sin \: 75 \: + \: sin \: 15}{cos \: 105 \: - \: cos \: 15} \\ = \frac{ 2 \: sin \: \frac{1}{2}(75 + 15)cos \: \frac{1}{2} (75 - 15) }{ - 2 \: sin \: \frac{1}{2}(105 + 15) \: sin \: \frac{1}{2} (105 - 15) } \\ = \frac{2 \: sin \: \frac{1}{2} (90)cos \: \frac{1}{2} (60)}{ - 2sin \frac{1}{2} \: (120)sin \: \frac{1}{2}(90) } \\ = \frac{2sin \: (45)cos (30)}{ - 2sin \: (60)sin \: (45)} \\ = - \frac{(cos \: (30)}{sin \: (60) } \\ = - \frac{ \frac{1}{2} \sqrt{3} }{ \frac{1}{2 } \sqrt{3} } \\ = - 1[/tex]