operatorname{cotg}(2x-pi)=operatorname{cotg}(x+pi/3) eching

$$\operatorname { cotg } ( 2 x - \pi ) = \operatorname { cotg } ( x + \frac { \pi } { 3 } )$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{4\pi }{3}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }g=\pi n_{1}\\x\in \mathrm{R}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }g=\pi n_{2}+\frac{\pi }{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$3\cot(g)\left(2x-\pi \right)=3\cot(g)\left(x+\frac{\pi }{3}\right)$$

3\cot(g) ga 2x-\pi ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6\cot(g)x-3\cot(g)\pi =3\cot(g)\left(x+\frac{\pi }{3}\right)$$

3\cot(g) ga x+\frac{\pi }{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6\cot(g)x-3\cot(g)\pi =3\cot(g)x+3\cot(g)\times \frac{\pi }{3}$$

3\times \frac{\pi }{3} ni yagona kasrga aylantiring.

$$6\cot(g)x-3\cot(g)\pi =3\cot(g)x+\frac{3\pi }{3}\cot(g)$$

3 va 3 ni qisqartiring.

$$6\cot(g)x-3\cot(g)\pi =3\cot(g)x+\pi \cot(g)$$

Ikkala tarafdan 3\cot(g)x ni ayirish.

$$6\cot(g)x-3\cot(g)\pi -3\cot(g)x=\pi \cot(g)$$

3\cot(g)x ni olish uchun 6\cot(g)x va -3\cot(g)x ni birlashtirish.

$$3\cot(g)x-3\cot(g)\pi =\pi \cot(g)$$

3\cot(g)\pi ni ikki tarafga qo’shing.

$$3\cot(g)x=\pi \cot(g)+3\cot(g)\pi$$

4\pi \cot(g) ni olish uchun \pi \cot(g) va 3\cot(g)\pi ni birlashtirish.

$$3\cot(g)x=4\pi \cot(g)$$

Ikki tarafini 3\cot(g) ga bo‘ling.

$$\frac{3\cot(g)x}{3\cot(g)}=\frac{4\pi \cot(g)}{3\cot(g)}$$

3\cot(g) ga bo'lish 3\cot(g) ga ko'paytirishni bekor qiladi.

$$x=\frac{4\pi \cot(g)}{3\cot(g)}$$

4\pi \cot(g) ni 3\cot(g) ga bo'lish.

$$x=\frac{4\pi }{3}$$

g uchun yechish

$$\left\{\begin{matrix}\\g=\pi n_{1}+\frac{\pi }{2}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\g\neq \pi n_{2}\text{, }\forall n_{2}\in \mathrm{Z}\text{, }&x=\frac{4\pi }{3}\end{matrix}\right,$$