Вариант 2 1. Вычислить sin 103°30′ cos 13°30′ - sin 13°30′ cos 103°30′. cos 53° cos 8° + sin 53° sin 8°. π π π π sin cos + cos sin . 12 6 12 6 8π 8π 8π 8π cos cos - sin sin .

Ответ: -1; \(\frac{\sqrt{2}}{2}\); \(\frac{\sqrt{3}}{2}\); 1

1. sin 103°30′ cos 13°30′ - sin 13°30′ cos 103°30′ = sin(103°30′ - 13°30′) = sin(90°) = -1
2. cos 53° cos 8° + sin 53° sin 8° = cos(53° - 8°) = cos(45°) = \(\frac{\sqrt{2}}{2}\)
3. sin \(\frac{π}{12}\) cos \(\frac{π}{6}\) + cos \(\frac{π}{12}\) sin \(\frac{π}{6}\) = sin(\( \frac{π}{12} + \frac{π}{6}\)) = sin(\( \frac{π}{12} + \frac{2π}{12}\)) = sin(\( \frac{3π}{12}\)) = sin(\( \frac{π}{4}\)) = \(\frac{\sqrt{2}}{2}\)
4. cos \(\frac{π}{9}\) cos \(\frac{8π}{9}\) - sin \(\frac{π}{9}\) sin \(\frac{8π}{9}\) = cos(\( \frac{π}{9} + \frac{8π}{9}\)) = cos(\( \frac{9π}{9}\)) = cos(π) = -1

Ответ: -1; \(\frac{\sqrt{2}}{2}\); \(\frac{\sqrt{3}}{2}\); 1