Solve for x (complex solution)
x=-i\ln(\frac{\left(-1-i\right)\sqrt{y^{2}-2}+\left(1+i\right)y}{2})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}
x=-i\ln(\left(\frac{1}{2}+\frac{1}{2}i\right)\left(\sqrt{y^{2}-2}+y\right))+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}
Solve for y (complex solution)
y=\left(\frac{1}{2}-\frac{1}{2}i\right)e^{ix}+\left(\frac{1}{2}+\frac{1}{2}i\right)e^{-ix}
Solve for y
y=\sin(x)+\cos(x)
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