Solve operatorname{cotg}(θ/2)=2s/D

$$\operatorname { cotg } ( \theta / 2 ) = 2 s / D$$

Solve for D

$$\left\{\begin{matrix}D=\frac{4s\tan(g)}{\theta }\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\left(g>\frac{\pi n_{3}}{2}\text{ and }g<\frac{\pi n_{3}}{2}+\frac{\pi }{2}\right)\text{ and }\theta \neq 0\text{ and }s\neq 0\\D\neq 0\text{, }&\left(\exists n_{2}\in \mathrm{Z}\text{ : }g=\pi n_{2}+\frac{\pi }{2}\text{ and }s=0\right)\text{ or }\left(\theta =0\text{ and }s=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }g=\pi n_{1}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable D cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2D, the least common multiple of 2,D.

$$\cot(g)D\theta =2\times 2s$$

Multiply 2 and 2 to get 4.

$$\cot(g)D\theta =4s$$

The equation is in standard form.

$$\theta \cot(g)D=4s$$

Divide both sides by \cot(g)\theta .

$$\frac{\theta \cot(g)D}{\theta \cot(g)}=\frac{4s}{\theta \cot(g)}$$

Dividing by \cot(g)\theta undoes the multiplication by \cot(g)\theta .

$$D=\frac{4s}{\theta \cot(g)}$$

Divide 4s by \cot(g)\theta .

$$D=\frac{4s\tan(g)}{\theta }$$

Variable D cannot be equal to 0.

$$D=\frac{4s\tan(g)}{\theta }\text{, }D\neq 0$$