Упр.22.3 ГДЗ Мордкович 10-11 класс (Алгебра)

a) sin РїРё/5 — sin РїРё/10;
6) sin РїРё/3 + sin РїРё/4;
РІ) sin РїРё/6 + sin РїРё/7;
Рі) sin РїРё/3 — sin РїРё/11.

1. $$\sin \frac{\pi}{5}-\sin \frac{\pi}{10}=2\cos \frac{\frac{\pi}{5}+\frac{\pi}{10}}{2}\sin \frac{\frac{\pi}{5}-\frac{\pi}{10}}{2}=2\cos \frac{3\pi}{20}\sin \frac{\pi}{20}.$$
2. $$\sin \frac{\pi}{3}+\sin \frac{\pi}{4}=2\sin \frac{\frac{\pi}{3}+\frac{\pi}{4}}{2}\cos \frac{\frac{\pi}{3}-\frac{\pi}{4}}{2}=2\sin \frac{7\pi}{24}\cos \frac{\pi}{24}.$$
3. $$\sin \frac{\pi}{6}+\sin \frac{\pi}{7}=2\sin \frac{\frac{\pi}{6}+\frac{\pi}{7}}{2}\cos \frac{\frac{\pi}{6}-\frac{\pi}{7}}{2}=2\sin \frac{13\pi}{84}\cos \frac{\pi}{84}.$$
4. $$\sin \frac{\pi}{3}-\sin \frac{\pi}{11}=2\cos \frac{\frac{\pi}{3}+\frac{\pi}{11}}{2}\sin \frac{\frac{\pi}{3}-\frac{\pi}{11}}{2}=2\cos \frac{7\pi}{33}\sin \frac{4\pi}{33}.$$

Ответ

а) $$2\cos \frac{3\pi}{20}\sin \frac{\pi}{20}$$
б) $$2\sin \frac{7\pi}{24}\cos \frac{\pi}{24}$$
в) $$2\sin \frac{13\pi}{84}\cos \frac{\pi}{84}$$
г) $$2\cos \frac{7\pi}{33}\sin \frac{4\pi}{33}$$