Ratkaise sin(x)+cos(y)=3

$$\sin ( x ) + \cos ( y ) = 3$$

Ratkaise muuttujan x suhteen

$$\left\{\begin{matrix}x=-i\ln(\frac{-2i\cos(y)-\sqrt{2}\sqrt{12\cos(y)-\cos(2y)-17}+6i}{2})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\frac{-2i\cos(y)-\sqrt{2}\sqrt{12\cos(y)-\cos(2y)-17}+6i}{2}\neq 0\\x=-i\ln(\frac{-2i\cos(y)+\sqrt{2}\sqrt{12\cos(y)-\cos(2y)-17}+6i}{2})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&\frac{-2i\cos(y)+\sqrt{2}\sqrt{12\cos(y)-\cos(2y)-17}+6i}{2}\neq 0\end{matrix}\right,$$

Ratkaise muuttujan y suhteen

$$\left\{\begin{matrix}y=-i\ln(\frac{-2\sin(x)-\sqrt{2}\sqrt{-\cos(2x)-12\sin(x)+17}+6}{2})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\frac{-2\sin(x)-\sqrt{2}\sqrt{-\cos(2x)-12\sin(x)+17}+6}{2}\neq 0\\y=-i\ln(\frac{-2\sin(x)+\sqrt{2}\sqrt{-\cos(2x)-12\sin(x)+17}+6}{2})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&\frac{-2\sin(x)+\sqrt{2}\sqrt{-\cos(2x)-12\sin(x)+17}+6}{2}\neq 0\end{matrix}\right,$$