Вычислите sin67°30'.

\[\sin{67{^\circ}30^{'}} = \sqrt{\frac{1 - \cos{135{^\circ}}}{2}} =\]

\[= \sqrt{\frac{1 - \cos(\pi - 45{^\circ})}{2}} =\]

\[= \sqrt{\frac{1 + \cos{45{^\circ}}}{2}} = \sqrt{\frac{1 + \frac{\sqrt{2}}{2}}{2}} =\]

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