Упр.1121 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) cos 23pi/4 — sin 15pi/4
2) sin 25pi/3 — tg 10pi/3
3) 3cos 3660 +sin(-1560)
4) cos(-945)+tg 1035

1. $$\cos \frac{23\pi}{4}-\sin \frac{15\pi}{4}=\cos \left(6\pi-\frac{\pi}{4}\right)-\sin \left(4\pi-\frac{\pi}{4}\right)$$
   $$=\cos \frac{\pi}{4}+\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=\sqrt{2}.$$

2. $$\sin \frac{25\pi}{3}-\tg \frac{10\pi}{3}=\sin \left(8\pi+\frac{\pi}{3}\right)-\tg \left(3\pi+\frac{\pi}{3}\right)$$
   $$=\sin \frac{\pi}{3}-\tg \frac{\pi}{3}=\frac{\sqrt{3}}{2}-\sqrt{3}=-\frac{\sqrt{3}}{2}.$$

3. $$3\cos 3660^\circ+\sin(-1560^\circ)=3\cos(3600^\circ+60^\circ)+\sin(-1800^\circ+240^\circ)$$
   $$=3\cos 60^\circ+\sin 240^\circ=3\cdot \frac12+\sin(180^\circ+60^\circ)$$
   $$=\frac32-\sin 60^\circ=\frac32-\frac{\sqrt{3}}{2}=\frac{3-\sqrt{3}}{2}.$$

4. $$\cos(-945^\circ)+\tg 1035^\circ=\cos(-1080^\circ+135^\circ)+\tg(900^\circ+135^\circ)$$
   $$=\cos 135^\circ+\tg 135^\circ=\cos(90^\circ+45^\circ)+\tg(90^\circ+45^\circ)$$
   $$=-\sin 45^\circ-1=-\frac{\sqrt{2}}{2}-1=-\frac{\sqrt{2}+2}{2}.$$

Ответ

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