Cos75+cos15/sin75-sin15

[tex] \frac{cos \: 75 \: + \: cos \: 15}{sin \: 75 - sin \: 15} \\ \\ = \frac{2 \: cos \: \frac{1}{2} \: (75 + 15) \: cos \: \frac{1}{2}(75 - 15) }{2 \: cos \: \frac{1}{2}(75 + 15)sin \: \frac{1}{2} (75 - 15)} \\ \\ = \frac{2cos \: \frac{1}{2}(90) \: cos \: \frac{1}{2}(60) }{2 \: cos \: \frac{1}{2} (90)sin \: \frac{1}{2} (60)} \\ \\ = \frac{2 \: cos \: (45) \: cos \: (30)}{ \: 2cos \: (45) \: sin \: (30)} \\ \\ = \frac{2( \frac{1}{2} \sqrt{2} )( \frac{1}{2} \sqrt{3} ) }{2 \: ( \frac{1}{2} \sqrt{2} ) \: ( \frac{1}{2} )} \\ \\ = \frac{ \frac{1}{2} \sqrt{6} }{ \frac{1}{2} \sqrt{2} } \\ \\ = \frac{ \sqrt{6} }{ \sqrt{2} } \\ \\ = \sqrt{ \frac{6}{2} } \\ \\= \sqrt{3} [/tex]