Задание 14.8

Question

Найдите значение выражения $\dfrac{\cos 64^{\circ} \cos 4^{\circ}-\cos 86^{\circ} \cos 26^{\circ}}{\cos 71^{\circ} \cos 41^{\circ}-\cos 49^{\circ} \cos 19^{\circ}}$.

Gimli · Accepted Answer

$$ \frac{\cos 64^{\circ} \cdot \cos 4^{\circ}-\cos 86^{\circ} \cos 26^{\circ}}{\cos 71^{\circ} \cdot \cos 41^{\circ}-\cos 49^{\circ} \cdot \cos 19^{\circ}}= \frac{\cos 64^{\circ} \cos 4^{\circ}-\sin 4^{\circ} \sin 64^{\circ}}{\cos 71^{\circ} \cos 41^{\circ}-\sin 41^{\circ} \sin 71^{\circ}}= \frac{\cos \left(64^{\circ}+4^{\circ}\right)}{\cos \left(71^{\circ}+41^{\circ}\right)}=\frac{\cos 68^{\circ}}{\cos 112^{\circ}}=$$ $$= \frac{\cos 68^{\circ}}{\cos \left(180^{\circ}-68^{\circ}\right)}=\frac{\cos 68^{\circ}}{-\cos 68^{\circ}}=-1 $$

Задание 14.8

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Задание 14.8

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