Вариант 1 1. Вычислить sin 42°30′ cos 47°30' + sin 47°30′ cos 42°30′. cos 27° cos 18° - sin 27° sin 18°. π sin cos π 5 15 5 15 4π 5π 4π 5π cos cos + sin sin . 9 18 9 18

Ответ: 1; 1/2; \(\frac{\sqrt{2}}{2}\)

1. sin 42°30′ cos 47°30′ + sin 47°30′ cos 42°30′ = sin(42°30′ + 47°30′) = sin(90°) = 1
2. cos 27° cos 18° - sin 27° sin 18° = cos(27° + 18°) = cos(45°) = \(\frac{\sqrt{2}}{2}\)
3. sin \(\frac{π}{5}\) cos \(\frac{π}{15}\) - cos \(\frac{2π}{5}\) sin \(\frac{π}{15}\) = sin(\( \frac{π}{5} - \frac{π}{15}\)) = sin(\( \frac{3π - π}{15}\)) = sin(\( \frac{2π}{15}\)) = sin(\( \frac{π}{15} + \frac{π}{15}\)) = \(\frac{1}{2}\)
4. cos \(\frac{4π}{9}\) cos \(\frac{5π}{18}\) + sin \(\frac{4π}{9}\) sin \(\frac{5π}{18}\) = cos(\( \frac{4π}{9} - \frac{5π}{18}\)) = cos(\( \frac{8π - 5π}{18}\)) = cos(\( \frac{3π}{18}\)) = cos(\( \frac{π}{6}\)) = \(\frac{\sqrt{3}}{2}\)

Ответ: 1; 1/2; \(\frac{\sqrt{2}}{2}\)