Solve y=log(sinx/1+cosx)8

$$y = \log ( \frac { \sin x } { 1 + \cos x } ) 8$$

Solve for x

$$\left\{\begin{matrix}x=\arcsin(\frac{2\times 10^{\frac{y}{8}}}{10^{\frac{y}{4}}+1})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }\exists n_{3}\in \mathrm{Z}\text{ : }\left(n_{3}<\frac{\frac{\arcsin(\frac{2\times 10^{\frac{y}{8}}}{10^{\frac{y}{4}}+1})}{\pi }+2n_{1}}{2}\text{ and }n_{1}\leq n_{3}\right)\text{, }&y\leq 0\\x=-\arcsin(\frac{2\times 10^{\frac{y}{8}}}{10^{\frac{y}{4}}+1})+2\pi n_{2}+\pi \text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{3}\in \mathrm{Z}\text{ : }\left(n_{2}\geq n_{3}\text{ and }n_{2}<\frac{\frac{\arcsin(\frac{2\times 10^{\frac{y}{8}}}{10^{\frac{y}{4}}+1})}{\pi }+2n_{3}}{2}\right)\text{, }&y\geq 0\end{matrix}\right.$$

Solve for y

$$y=8\log(\tan(\frac{x}{2}))$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(x>2\pi n_{1}\text{ and }x<2\pi n_{1}+\pi \right)$$