Whakaoti i te operatorname{cotg}(2x-pi)=operatorname{cotg}(x+pi/3)

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

Whakaoti mō x

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3\cot(g) ki te 2x-\pi .

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3\cot(g) ki te x+\frac{\pi }{3}.

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

Tuhia te 3\times \frac{\pi }{3} hei hautanga kotahi.

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

Me whakakore te 3 me te 3.

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

Tangohia te 3\cot(g)x mai i ngā taha e rua.

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

Pahekotia te 6\cot(g)x me -3\cot(g)x, ka 3\cot(g)x.

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

Me tāpiri te 3\cot(g)\pi ki ngā taha e rua.

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

Pahekotia te \pi \cot(g) me 3\cot(g)\pi , ka 4\pi \cot(g).

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

Whakawehea ngā taha e rua ki te 3\cot(g).

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

Mā te whakawehe ki te 3\cot(g) ka wetekia te whakareanga ki te 3\cot(g).

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

Whakawehe 4\pi \cot(g) ki te 3\cot(g).

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

Whakaoti mō g

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