Leysa cscA-cotA=1/x

$$\csc A - \cot A = \frac { 1 } { x }$$

Leystu fyrir x (complex solution)

$$\left\{\begin{matrix}x=\frac{i\sin(A)}{-i\cos(A)+i}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }A=\pi n_{1}\\x\neq 0\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }A=2\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }A=\pi n_{1}\end{matrix}\right.$$

Leystu fyrir A

$$\left\{\begin{matrix}A=\arcsin(\frac{2x}{x^{2}+1})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}>\frac{\arcsin(\frac{2x}{x^{2}+1})}{\pi }+2n_{2}-1\text{ and }n_{1}<\frac{\arcsin(\frac{2x}{x^{2}+1})}{\pi }+2n_{2}\right)\text{, }&|x|\geq 1\\A=-\arcsin(\frac{2x}{x^{2}+1})+2\pi n_{3}+\pi \text{, }n_{3}\in \mathrm{Z}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}>-\frac{\arcsin(\frac{2x}{x^{2}+1})}{\pi }+2n_{3}\text{ and }n_{1}<-\frac{\arcsin(\frac{2x}{x^{2}+1})}{\pi }+2n_{3}+1\right)\text{, }&|x|\leq 1\text{ and }x\neq 0\end{matrix}\right.$$

Leystu fyrir x

$$x=\cot(\frac{A}{2})$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(A>\pi n_{1}\text{ and }A<\pi n_{1}+\pi \right)$$