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

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

Lahendage ja leidke x

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

Juhised lineaarvõrrandi lahendamiseks

Korrutage võrrandi mõlemad pooled 3-ga.

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

Kasutage distributiivsusomadust, et korrutada 3\cot(g) ja 2x-\pi .

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

Kasutage distributiivsusomadust, et korrutada 3\cot(g) ja x+\frac{\pi }{3}.

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

Avaldage 3\times \frac{\pi }{3} ühe murdarvuna.

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

Taandage 3 ja 3.

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

Lahutage mõlemast poolest 3\cot(g)x.

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

Kombineerige 6\cot(g)x ja -3\cot(g)x, et leida 3\cot(g)x.

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

Liitke 3\cot(g)\pi mõlemale poolele.

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

Kombineerige \pi \cot(g) ja 3\cot(g)\pi , et leida 4\pi \cot(g).

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

Jagage mõlemad pooled 3\cot(g)-ga.

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

3\cot(g)-ga jagamine võtab 3\cot(g)-ga korrutamise tagasi.

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

Jagage 4\pi \cot(g) väärtusega 3\cot(g).

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

Lahendage ja leidke g

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