Упр.1049 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) 2sin75°*cos75°
2) cos^2 75°-sin^2 75°

1. $$2\sin 75^\circ \cos 75^\circ=\sin 150^\circ=\sin 30^\circ=\frac12.$$

2. $$\cos^2 75^\circ-\sin^2 75^\circ=\cos 150^\circ=-\cos 30^\circ=-\frac{\sqrt3}{2}.$$

3. $$\frac{6\tg 75^\circ}{1-\tg^2 75^\circ}=3\cdot \frac{2\tg 75^\circ}{1-\tg^2 75^\circ}=3\tg(2\cdot 75^\circ)=3\tg 150^\circ=-3\tg 30^\circ=-3\cdot \frac{\sqrt3}{3}=-\sqrt3.$$

4. $$\frac{\tg^2 22^\circ 30′-1}{\tg 22^\circ 30′}=-2\cdot \frac{1-\tg^2 22^\circ 30′}{2\tg 22^\circ 30′}=-2\left(\tg(2\cdot 22^\circ 30′)\right)^{-1}=-2\left(\tg 45^\circ\right)^{-1}=-2.$$

Ответ

$$\frac12,\ -\frac{\sqrt3}{2},\ -\sqrt3,\ -2.$$