[tex] \frac{\pi}{12} = \frac{180}{12}^{\circ} = 15^{\circ} \\ \\ sin15^{\circ} = sin(45-30) = sin45\cdot cos30 - cos45\cdot sin30 = \\ = \frac{ \sqrt{2} }{2} \cdot\frac{ \sqrt{3} }{2} - \frac{ \sqrt{2} }{2} \cdot \frac{ 1 }{2} = \frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4} = \frac{ \sqrt{6}- \sqrt{2} }{4} [/tex]
