Factor; Then Use Fundamental Identities to Simplify the Expression Below $\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alpha$

Multiple Choice

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$\cot ^ { 2 } \alpha + \cot ^ { 2 } \alpha \cdot \tan ^ { 2 } \alpha$

A) $\csc ^ { 2 } \alpha$
B) $1 + \cot ^ { 2 } \alpha$
C) $\sec ^ { 2 } \alpha$
D) $1 / \cos ^ { 2 } \left( \frac { \pi } { 2 } - \alpha \right)$
E) $\frac { 1 } { 1 - \cos ^ { 2 } \alpha }$