Solve operatorname{cog}sqrt{1+x}+3logsqrt{1-x}=logsqrt{1-x^2}+2

$$\operatorname { cog } \sqrt { 1 + x } + 3 \log \sqrt { 1 - x } = \log \sqrt { 1 - x ^ { 2 } } + 2$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-\frac{\left(x+1\right)^{-\frac{1}{2}}\left(-\log(\sqrt{1-x^{2}})+3\log(\sqrt{1-x})-2\right)}{go}\text{, }&x\neq -1\text{ and }g\neq 0\text{ and }o\neq 0\text{ and }x\neq 1\\c\in \mathrm{C}\text{, }&x=5001-300\sqrt{278}\text{ and }\left(g=0\text{ or }o=0\right)\end{matrix}\right.$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{\left(x+1\right)^{-\frac{1}{2}}\left(-\log(\sqrt{1-x^{2}})+3\log(\sqrt{1-x})-2\right)}{co}\text{, }&x\neq -1\text{ and }o\neq 0\text{ and }c\neq 0\text{ and }x\neq 1\\g\in \mathrm{C}\text{, }&x=5001-300\sqrt{278}\text{ and }\left(o=0\text{ or }c=0\right)\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{-\log(1-x^{2})+3\log(1-x)-4}{2\sqrt{x+1}go}\text{, }&g\neq 0\text{ and }o\neq 0\text{ and }|x|<1\\c\in \mathrm{R}\text{, }&\left(g=0\text{ or }o=0\right)\text{ and }x=5001-300\sqrt{278}\end{matrix}\right.$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{-\log(1-x^{2})+3\log(1-x)-4}{2\sqrt{x+1}co}\text{, }&o\neq 0\text{ and }c\neq 0\text{ and }|x|<1\\g\in \mathrm{R}\text{, }&\left(o=0\text{ or }c=0\right)\text{ and }x=5001-300\sqrt{278}\end{matrix}\right.$$