Задание 14.7

Question

Вычислите значение выражения:
\begin{enumerate}
\item $\dfrac{\sin ^{2} 315^{\circ} \cos 300^{\circ}+\operatorname{tg}\left(-315^{\circ}\right)}{\sin \left(-120^{\circ}\right) \cos 150^{\circ}}$
\item $\dfrac{\cos 66^{\circ} \cos 6^{\circ}+\cos 84^{\circ} \cos 24^{\circ}}{\cos 65^{\circ} \cos 5^{\circ}+\cos 85^{\circ} \cos 25^{\circ}}$.
\end{enumerate}

Gimli · Accepted Answer

\begin{enumerate}
\item
$$

\frac{\sin ^{2} 315^{\circ} \cos 300^{\circ}+\operatorname{tg}\left(-315^{\circ}\right)}{\sin \left(-120^{\circ}\right) \cos 150^{\circ}}= \frac{\left(-\cos 45^{\circ}\right)^{2} \cdot \sin 30^{\circ}+\operatorname{tg} 45^{\circ}}{-\cos 30^{\circ} \cdot\left(-\cos 30^{\circ}\right)}= \frac{\left(\frac{\sqrt{2}}{2}\right)^{2} \cdot \frac{1}{2}+1}{-\frac{\sqrt{3}}{2} \cdot\left(-\frac{\sqrt{3}}{2}\right)}=\frac{\frac{1}{4}+1}{\frac{3}{4}}=\frac{5}{4}: \frac{3}{4}=\frac{5}{3}

$$
\item $$

\frac{\cos 66^{\circ} \cos 6^{\circ}+\cos 84^{\circ} \cos 24^{\circ}}{\cos 65^{\circ} \cos 5^{\circ}+\cos 85^{\circ} \cdot \cos 25^{\circ}}=\frac{\sin 24^{\circ} \cdot \sin 84^{\circ}+\cos 84^{\circ} \cdot \cos 24^{\circ}}{\sin 25^{\circ} \cdot \sin 85^{\circ}+\cos 85^{\circ} \cos 25^{\circ}}= \frac{\cos \left(84^{\circ}-24^{\circ}\right)}{\cos \left(85^{\circ}-25^{\circ}\right)}=\frac{\cos 60^{\circ}}{\cos 60^{\circ}}=1
$$
\end{enumerate}

Задание 14.7

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Задание 14.7

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