Упр.6.10 ГДЗ Мордкович 10-11 класс (Алгебра)

a) tg(РїРё/5) * ctg(РїРё/5);
6) 3tg(2,3) * ctg(2,3);
РІ) tg(РїРё/7) * ctg(РїРё/7);
Рі) 7tg(РїРё/12) * ctg(РїРё/12).

1. $$\tg \frac{\pi}{5}\cdot \ctg \frac{\pi}{5}=\frac{\sin \frac{\pi}{5}}{\cos \frac{\pi}{5}}\cdot \frac{\cos \frac{\pi}{5}}{\sin \frac{\pi}{5}}=1$$

2. $$3\tg 2{,}3\cdot \ctg 2{,}3=3\cdot \frac{\sin 2{,}3}{\cos 2{,}3}\cdot \frac{\cos 2{,}3}{\sin 2{,}3}=3$$

3. $$\tg \frac{\pi}{7}\cdot \ctg \frac{\pi}{7}=\frac{\sin \frac{\pi}{7}}{\cos \frac{\pi}{7}}\cdot \frac{\cos \frac{\pi}{7}}{\sin \frac{\pi}{7}}=1$$

4. $$7\tg \frac{\pi}{12}\cdot \ctg \frac{\pi}{12}=7\cdot \frac{\sin \frac{\pi}{12}}{\cos \frac{\pi}{12}}\cdot \frac{\cos \frac{\pi}{12}}{\sin \frac{\pi}{12}}=7$$

Ответ

а) $$1$$; б) $$3$$; в) $$1$$; г) $$7$$.