Question

$$\cos \theta = \frac { 2 M } { 1 + M ^ { 2 } } , \sec \theta =$$

Solve for θ, M, a

$\theta =\arccos(\frac{1}{a})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }M=\frac{a(\sqrt{a^{2}-1}+|a|)}{|a|}\text{, }a\in (-\infty,-1]\cup [1,\infty)\text{; }\theta =\arccos(\frac{1}{a})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }M=\frac{a(-\sqrt{a^{2}-1}+|a|)}{|a|}\text{, }a\in (-\infty,-1]\cup [1,\infty)\text{; }\theta =-\arccos(\frac{1}{a})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }M=\frac{a(\sqrt{a^{2}-1}+|a|)}{|a|}\text{, }a\in (-\infty,-1]\cup [1,\infty)\text{; }\theta =-\arccos(\frac{1}{a})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }M=\frac{a(-\sqrt{a^{2}-1}+|a|)}{|a|}\text{, }a\in (-\infty,-1]\cup [1,\infty)$