Issolvi y=sin(A+B)

$$y = \sin ( A + B )$$

Solvi għal A (complex solution)

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

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

Solvi għal B (complex solution)

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

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

Solvi għal A

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

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

Solvi għal B

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

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