Упр.485 ГДЗ Алимов 10-11 класс (Алгебра)

1) sin 73° cos 17° + cos 73° sin 17°;
2) sin 73° cos 13° — cos 73° sin 13°;
3) sin 5пи/12 * cos пи/12 + sin пи/12* cos 5пи/12;
4) sin 7пи/12 * cos пи/12 — sin пи/12* cos 7пи/12.

1. $$\sin 73^\circ \cos 17^\circ + \cos 73^\circ \sin 17^\circ = \sin(73^\circ+17^\circ)=\sin 90^\circ=1$$

2. $$\sin 73^\circ \cos 13^\circ — \cos 73^\circ \sin 13^\circ = \sin(73^\circ-13^\circ)=\sin 60^\circ=\frac{\sqrt{3}}{2}$$

3. $$\sin \frac{5\pi}{12}\cos \frac{\pi}{12}+\sin \frac{\pi}{12}\cos \frac{5\pi}{12}=\sin\left(\frac{5\pi}{12}+\frac{\pi}{12}\right)=\sin \frac{\pi}{2}=1$$

4. $$\sin \frac{7\pi}{12}\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\cos \frac{7\pi}{12}=\sin\left(\frac{7\pi}{12}-\frac{\pi}{12}\right)=\sin \frac{\pi}{2}=1$$

Ответ

1) $$1$$; 2) $$\frac{\sqrt{3}}{2}$$; 3) $$1$$; 4) $$1$$.