समाधान y=sin(x+c)

$$y = \sin ( x + c )$$

c को लागि हल गर्नुहोस् (complex solution)

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

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

x को लागि हल गर्नुहोस् (complex solution)

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

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

c को लागि हल गर्नुहोस्

$$c=\arcsin(y)+2\pi n_{1}-x\text{, }n_{1}\in \mathrm{Z}$$

$$c=-\arcsin(y)+2\pi n_{2}-x+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 1$$

x को लागि हल गर्नुहोस्

$$x=\arcsin(y)+2\pi n_{1}-c\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\arcsin(y)+2\pi n_{2}-c+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 1$$