Let $S$ be the set of those real numbers $x$ for which the identity $$\sum _ { n = 2 } ^ { \infty } \cos ^ { n } x = ( 1 + \cos x ) \cot ^ { 2 } x$$ is valid, and the quantities on both sides are finite. Then (A) $S$ is the empty set. (B) $S = \{ x \in \mathbb { R } : x \neq n \pi$ for all $n \in \mathbb { Z } \}$. (C) $S = \{ x \in \mathbb { R } : x \neq 2 n \pi$ for all $n \in \mathbb { Z } \}$. (D) $S = \{ x \in \mathbb { R } : x \neq ( 2 n + 1 ) \pi$ for all $n \in \mathbb { Z } \}$.
Let $S$ be the set of those real numbers $x$ for which the identity
$$\sum _ { n = 2 } ^ { \infty } \cos ^ { n } x = ( 1 + \cos x ) \cot ^ { 2 } x$$
is valid, and the quantities on both sides are finite. Then\\
(A) $S$ is the empty set.\\
(B) $S = \{ x \in \mathbb { R } : x \neq n \pi$ for all $n \in \mathbb { Z } \}$.\\
(C) $S = \{ x \in \mathbb { R } : x \neq 2 n \pi$ for all $n \in \mathbb { Z } \}$.\\
(D) $S = \{ x \in \mathbb { R } : x \neq ( 2 n + 1 ) \pi$ for all $n \in \mathbb { Z } \}$.