Leysa {l}{cosx=siny}{sin^2y-cosx=2}

$$\left\{ \begin{array} { l } { \cos x = \sin y } \\ { \sin ^ { 2 } y - \cos x = 2 } \end{array} \right.$$

Leystu fyrir x, y (complex solution)

$$x=2\pi n_{1}-i\ln(2-\sqrt{3})\text{, }n_{1}\in \mathrm{Z}\text{, }y=2\pi n_{2}-i\ln(-\sqrt{3}i+2i)\text{, }n_{2}\in \mathrm{Z}$$

$$x=2\pi n_{1}-i\ln(2-\sqrt{3})\text{, }n_{1}\in \mathrm{Z}\text{, }y=2\pi n_{3}-i\ln(\sqrt{3}i+2i)\text{, }n_{3}\in \mathrm{Z}$$

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

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

$$x=2\pi n_{5}+\pi \text{, }n_{5}\in \mathrm{Z}\text{, }y=2\pi n_{6}+\frac{3\pi }{2}\text{, }n_{6}\in \mathrm{Z}$$

Leystu fyrir x, y

$$x=2\pi n_{1}+\pi$$

$$n_{1}\in \mathrm{Z}$$

$$y=2\pi n_{2}+\frac{3\pi }{2}$$

$$n_{2}\in \mathrm{Z}$$