გადაწყვიტეთ {l}{x+y=pi/4}{tanxtany=1/6}

$$\left\{ \begin{array} { l } { x + y = \frac { \pi } { 4 } } \\ { \tan x \tan y = \frac { 1 } { 6 } } \end{array} \right.$$

ამოხსნა x, y-ისთვის (complex solution)

$$x=\frac{8\pi n_{2}+\pi +4\arctan(\frac{1}{7})}{8}\text{, }n_{2}\in \mathrm{Z}\text{, }y=\frac{8\pi n_{1}+\pi -4\arctan(\frac{1}{7})}{8}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{8\pi n_{1}+\pi -4\arctan(\frac{1}{7})}{8}\text{, }n_{1}\in \mathrm{Z}\text{, }y=\frac{8\pi n_{2}+\pi +4\arctan(\frac{1}{7})}{8}\text{, }n_{2}\in \mathrm{Z}$$

ამოხსნა x, y-ისთვის

$$x=\frac{4\pi n_{3}-4\arcsin(\frac{\sqrt{5}}{5})+\pi }{4}\text{, }n_{3}\in \mathrm{Z}\text{, }y=\pi n_{2}+\arcsin(\frac{\sqrt{5}}{5})\text{, }n_{2}\in \mathrm{Z}$$

$$x=\frac{4\pi n_{4}-4\arcsin(\frac{\sqrt{10}}{10})+\pi }{4}\text{, }n_{4}\in \mathrm{Z}\text{, }y=\pi n_{1}+\arcsin(\frac{\sqrt{10}}{10})\text{, }n_{1}\in \mathrm{Z}$$