[latex] sin( \alpha + \pi /8)*cos( \alpha - \pi /24)[/latex]

[latex]sin( \alpha +\frac{\pi}{8})\cdot cos( \alpha -\frac{\pi}{24})=\\\\=\frac{1}{2}(sin( \alpha +\frac{\pi}{8}+ \alpha -\frac{\pi}{24})+sin( \alpha +\frac{\pi}{8}- \alpha +\frac{\pi}{24})=\\\\=\frac{1}{2}(sin(2 \alpha +\frac{\pi}{12})+sin\frac{\pi}{6})=\frac{1}{4}+\frac{1}{2}sin(2 \alpha +\frac{\pi}{12})[/latex]