Упр.22.7 ГДЗ Мордкович 10-11 класс (Алгебра)

a) (cos 68 — cos 22) / (sin 68 — sin 22);
6) (sin 130 + sin 110) / (cos 130 + cos 110).

а)

$$ \frac{\cos 68^\circ-\cos 22^\circ}{\sin 68^\circ-\sin 22^\circ} = \frac{-2\sin \frac{68^\circ+22^\circ}{2}\sin \frac{68^\circ-22^\circ}{2}} {2\cos \frac{68^\circ+22^\circ}{2}\sin \frac{68^\circ-22^\circ}{2}} $$

$$ = -\frac{\sin 45^\circ}{\cos 45^\circ} = -\tg 45^\circ = -1 $$

б)

$$ \frac{\sin 130^\circ+\sin 110^\circ}{\cos 130^\circ+\cos 110^\circ} = \frac{2\sin \frac{130^\circ+110^\circ}{2}\cos \frac{130^\circ-110^\circ}{2}} {2\cos \frac{130^\circ+110^\circ}{2}\cos \frac{130^\circ-110^\circ}{2}} $$

$$ = \frac{\sin 120^\circ}{\cos 120^\circ} = \tg 120^\circ = \tg(180^\circ-60^\circ) = -\tg 60^\circ = -\sqrt{3} $$

Ответ

а) $$-1$$; б) $$-\sqrt{3}$$.