Задание 13.27

Question

Упростите выражение:
1) $\frac{\cos 6 \alpha}{\sin 2 \alpha}+\frac{\sin 6 \alpha}{\cos 2 \alpha}$
2) $\frac{\operatorname{tg} \alpha}{1+\operatorname{tg} \alpha}+\frac{\operatorname{tg} \alpha}{1-\operatorname{tg} \alpha}$

Gimli · Accepted Answer

$$
	ext { 1) } \begin{array}{l}
\frac{\cos 6 \alpha}{\sin 2 \alpha}+\frac{\sin 6 \alpha}{\cos 2 \alpha}=\frac{\cos 6 \alpha \cos 2 \alpha+\sin 6 \alpha \sin 2 \alpha}{\sin 2 \alpha \cdot \cos 2 \alpha}= \
=\frac{\cos 4 \alpha}{\frac{\sin 4 \alpha}{2}}=\frac{2 \cos 4 \alpha}{\sin 4 \alpha}= \frac{2}{\operatorname{tg} 4\alpha}\
	ext { 2) } \frac{\operatorname{tg} \alpha}{1+\operatorname{tg} \alpha}+\frac{\operatorname{tg} \alpha}{1-\operatorname{tg} \alpha}=\frac{\operatorname{tg} \alpha-\operatorname{tg}^{2} \alpha+\operatorname{tg} \alpha+\operatorname{tg}^{2} \alpha}{1-\operatorname{tg}^{2} \alpha}= \
=\frac{2 \operatorname{tg} \alpha}{1-\operatorname{tg}^{2} \alpha}=\operatorname{tg} 2 \alpha .
\end{array}
$$

Задание 13.27

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Задание 13.27

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