Solve sec^2x=1/2operatornamecoc^2x+tan^2x

$$\sec ^ { 2 } x = \frac { 1 } { 2 } \operatorname { coc } ^ { 2 } x + \tan ^ { 2 } x$$

Solve for c (complex solution)

$$c=\sqrt[4]{2}io^{-\frac{1}{2}}x^{-\frac{1}{4}}$$

$$c=\sqrt[4]{2}o^{-\frac{1}{2}}x^{-\frac{1}{4}}$$

$$c=-\sqrt[4]{2}o^{-\frac{1}{2}}x^{-\frac{1}{4}}$$

$$c=-\sqrt[4]{2}io^{-\frac{1}{2}}x^{-\frac{1}{4}}\text{, }x\neq 0\text{ and }o\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$$

Solve for o (complex solution)

$$o=-\frac{\sqrt{2}x^{-\frac{1}{2}}}{c^{2}}$$

$$o=\frac{\sqrt{2}x^{-\frac{1}{2}}}{c^{2}}\text{, }x\neq 0\text{ and }c\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$$

Solve for c

$$\left\{\begin{matrix}c=\sqrt{-\frac{1}{o}}\sqrt[4]{\frac{2}{x}}\text{; }c=-\sqrt{-\frac{1}{o}}\sqrt[4]{\frac{2}{x}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }o<0\text{ and }x>0\\c=\frac{\sqrt[4]{\frac{2}{x}}}{\sqrt{o}}\text{; }c=-\frac{\sqrt[4]{\frac{2}{x}}}{\sqrt{o}}\text{, }&o>0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }x>0\end{matrix}\right.$$

Solve for o

$$o=\frac{\sqrt{\frac{2}{x}}}{c^{2}}$$

$$o=-\frac{\sqrt{\frac{2}{x}}}{c^{2}}\text{, }c\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }x>0$$