გადაწყვიტეთ y=tan(θ)/e/frac{pi{x}}

$$y= \frac{ \frac{ \tan ( \theta ) }{ e } }{ \frac{ \pi }{ x } }$$

ამოხსნა x-ისთვის (complex solution)

$$\left\{\begin{matrix}x=\frac{\pi y\left(e^{i\theta +1}+e^{-i\theta +1}\right)}{2\sin(\theta )}\text{, }&\nexists n_{3}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{3}}{2}\text{ and }e^{i\theta +1}+e^{-i\theta +1}\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&\left(e^{i\theta +1}+e^{-i\theta +1}=0\text{ or }y=0\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\theta =\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

ამოხსნა y-ისთვის (complex solution)

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

ამოხსნა x-ისთვის

$$\left\{\begin{matrix}x=e\pi y\cot(\theta )\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\left(\theta >\frac{\pi n_{3}}{2}\text{ and }\theta <\frac{\pi n_{3}}{2}+\frac{\pi }{2}\right)\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\theta =\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

ამოხსნა y-ისთვის

$$y=\frac{x\tan(\theta )}{e\pi }$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }x\neq 0$$