Упр.23.6 ГДЗ Мерзляк 10 класс Базовый уровень (Алгебра)

1) cos^2(22°30′)-sin^2(22°30′); 3) 2sin(3?/8)cos(3?/8);
2) (2tg(75°))/(1-tg^2(75°)); 4) 1-2cos^2(?/12).

1. $$\cos^2 22^\circ 30′ — \sin^2 22^\circ 30′ = \cos(2 \cdot 22^\circ 30′) = \cos 45^\circ = \frac{\sqrt{2}}{2}.$$

2. $$\frac{2\tg 75^\circ}{1-\tg^2 75^\circ}=\tg(2\cdot 75^\circ)=\tg 150^\circ=\tg(180^\circ-30^\circ)=-\tg 30^\circ=-\frac{\sqrt{3}}{3}.$$

3. $$2\sin \frac{3\pi}{8}\cos \frac{3\pi}{8}=\sin\left(2\cdot \frac{3\pi}{8}\right)=\sin \frac{3\pi}{4}=\sin\left(\pi-\frac{\pi}{4}\right)=\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}.$$

4. $$1-2\cos^2 \frac{\pi}{12}=-(2\cos^2 \frac{\pi}{12}-1)=-\cos\left(2\cdot \frac{\pi}{12}\right)=-\cos \frac{\pi}{6}=-\frac{\sqrt{3}}{2}.$$

Ответ

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