Find All Solutions to the Equation $$\cos ^ { 2 } x + 2 \cos x + 1 = 0$$

Multiple Choice

Find all solutions to the equation.
- $$\cos ^ { 2 } x + 2 \cos x + 1 = 0$$

A) $\left\{ \frac { \pi } { 4 } + 2 \mathrm { n } \pi , \frac { 3 \pi } { 4 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \right\}$
B) $\left\{ \frac { 3 \pi } { 2 } + 2 n \pi \mid n = 0 , \pm 1 , \pm 2 , \ldots . \right\}$
C) $\{ \pi + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \}$
D) $\{ \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots . \}$