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

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

Atrast x

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

Lineāra vienādojuma risināšanas darbības

Reiziniet vienādojuma abas puses ar 3.

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

Izmantojiet distributīvo īpašību, lai reizinātu 3\cot(g) ar 2x-\pi .

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

Izmantojiet distributīvo īpašību, lai reizinātu 3\cot(g) ar x+\frac{\pi }{3}.

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

Izsakiet 3\times \frac{\pi }{3} kā vienu daļskaitli.

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

Saīsiniet 3 un 3.

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

Atņemiet 3\cot(g)x no abām pusēm.

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

Savelciet 6\cot(g)x un -3\cot(g)x, lai iegūtu 3\cot(g)x.

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

Pievienot 3\cot(g)\pi abās pusēs.

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

Savelciet \pi \cot(g) un 3\cot(g)\pi , lai iegūtu 4\pi \cot(g).

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

Daliet abas puses ar 3\cot(g).

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

Dalīšana ar 3\cot(g) atsauc reizināšanu ar 3\cot(g).

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

Daliet 4\pi \cot(g) ar 3\cot(g).

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

Atrast g

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