Упр.1233 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) tg(2x+pi/4)=-1
2) tg(3x-pi/4)=1/v3
3) v3-tg(x-pi/5)=0
4) 1-tg(x+pi/7)=0

1. $$\tg\left(2x+\frac{\pi}{4}\right)=-1$$
   $$2x+\frac{\pi}{4}=-\frac{\pi}{4}+\pi n,\quad n\in\mathbb{Z}$$
   $$2x=-\frac{\pi}{2}+\pi n$$
   $$x=-\frac{\pi}{4}+\frac{\pi n}{2}$$
2. $$\tg\left(3x-\frac{\pi}{4}\right)=\frac{1}{\sqrt{3}}$$
   $$3x-\frac{\pi}{4}=\frac{\pi}{6}+\pi n,\quad n\in\mathbb{Z}$$
   $$3x=\frac{5\pi}{12}+\pi n$$
   $$x=\frac{5\pi}{36}+\frac{\pi n}{3}$$
3. $$\sqrt{3}-\tg\left(x-\frac{\pi}{5}\right)=0$$
   $$\tg\left(x-\frac{\pi}{5}\right)=\sqrt{3}$$
   $$x-\frac{\pi}{5}=\frac{\pi}{3}+\pi n,\quad n\in\mathbb{Z}$$
   $$x=\frac{8\pi}{15}+\pi n$$
4. $$1-\tg\left(x+\frac{\pi}{7}\right)=0$$
   $$\tg\left(x+\frac{\pi}{7}\right)=1$$
   $$x+\frac{\pi}{7}=\frac{\pi}{4}+\pi n,\quad n\in\mathbb{Z}$$
   $$x=\frac{3\pi}{28}+\pi n$$

Ответ

1) $$x=-\frac{\pi}{4}+\frac{\pi n}{2},\ n\in\mathbb{Z}$$
2) $$x=\frac{5\pi}{36}+\frac{\pi n}{3},\ n\in\mathbb{Z}$$
3) $$x=\frac{8\pi}{15}+\pi n,\ n\in\mathbb{Z}$$
4) $$x=\frac{3\pi}{28}+\pi n,\ n\in\mathbb{Z}$$