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

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

Réitigh do x. (complex solution)

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi 3.

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

Úsáid an t-airí dáileach chun 3\cot(g) a mhéadú faoi 2x-\pi .

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

Úsáid an t-airí dáileach chun 3\cot(g) a mhéadú faoi x+\frac{\pi }{3}.

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

Scríobh 3\times \frac{\pi }{3} mar chodán aonair.

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

Cealaigh 3 agus 3.

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

Bain 3\cot(g)x ón dá thaobh.

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

Comhcheangail 6\cot(g)x agus -3\cot(g)x chun 3\cot(g)x a fháil.

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

Cuir 3\cot(g)\pi leis an dá thaobh.

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

Comhcheangail \pi \cot(g) agus 3\cot(g)\pi chun 4\pi \cot(g) a fháil.

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

Roinn an dá thaobh faoi 3\cot(g).

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

Má roinntear é faoi 3\cot(g) cuirtear an iolrúchán faoi 3\cot(g) ar ceal.

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

Roinn 4\pi \cot(g) faoi 3\cot(g).

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

Réitigh do x.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi 3.

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

Úsáid an t-airí dáileach chun 3\cot(g) a mhéadú faoi 2x-\pi .

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

Úsáid an t-airí dáileach chun 3\cot(g) a mhéadú faoi x+\frac{\pi }{3}.

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

Scríobh 3\times \frac{\pi }{3} mar chodán aonair.

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

Cealaigh 3 agus 3.

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

Bain 3\cot(g)x ón dá thaobh.

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

Comhcheangail 6\cot(g)x agus -3\cot(g)x chun 3\cot(g)x a fháil.

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

Cuir 3\cot(g)\pi leis an dá thaobh.

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

Comhcheangail \pi \cot(g) agus 3\cot(g)\pi chun 4\pi \cot(g) a fháil.

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

Roinn an dá thaobh faoi 3\cot(g).

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

Má roinntear é faoi 3\cot(g) cuirtear an iolrúchán faoi 3\cot(g) ar ceal.

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

Roinn 4\pi \cot(g) faoi 3\cot(g).

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

Réitigh do g. (complex solution)

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

Réitigh do g.

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