Вычислите sin75°.

\[\sin{75{^\circ}} = \sqrt{\frac{1 - \cos{150{^\circ}}}{2}} =\]

\[= \sqrt{\frac{1 - \cos(\pi - 30{^\circ})}{2}} =\]

\[= \sqrt{\frac{1 + \cos{30{^\circ}}}{2}} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2}}{2}} =\]

\[= \sqrt{\frac{2 + \sqrt{3}}{4}} = \frac{\sqrt{2 + \sqrt{3}}}{2}\ \ \]