реши 4 и 5

Question

реши 4 и 5

Расшифровка фото нейросетью:
Пример 2
Вычислите:

1. sin 8π/7 cos π/7 - sin π/7 cos 8π/7

2. cos 57°30' cos 27°30' + sin 57°30' sin 27°30'

3. cos 19°30' cos 25°30' - sin 19°30' sin 25°30'

4. cos 7π/9 cos 11π/9 - sin 7π/9 sin 11π/9

5. cos 8π/7 cos π/7 + sin 8π/7 sin π/7

Answer

4) $\cos\frac{7\pi}{9}\cos\frac{11\pi}{9} - \sin\frac{7\pi}{9}\sin\frac{11\pi}{9} = \cos\left(\frac{7\pi}{9} + \frac{11\pi}{9}\right) = \cos 2\pi = 1$

5) $\cos\frac{8\pi}{7}\cos\frac{\pi}{7} + \sin\frac{8\pi}{7}\sin\frac{\pi}{7} = \cos\left(\frac{8\pi}{7} - \frac{\pi}{7}\right) = \cos \pi = -1$