Factor; Then Use Fundamental Identities to Simplify the Expression Below $$\csc ^ { 3 } x - \csc ^ { 2 } x - \csc x + 1$$

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$$\csc ^ { 3 } x - \csc ^ { 2 } x - \csc x + 1$$

A) $\csc x \cot ^ { 2 } x - \cot ^ { 2 } x$
B) $\cos ^ { 2 } x \left( \frac { 1 - \sin x } { \sin ^ { 3 } x } \right)$
C) $\frac { \cos ^ { 4 } x } { \sin ^ { 3 } x + \sin ^ { 4 } x }$
D) $\frac { 1 - \sin x - \sin ^ { 2 } x + \sin ^ { 3 } x } { \sin ^ { 3 } x }$
E) $\frac { \sec ^ { 2 } x + \tan ^ { 2 } x } { \csc x }$

Correct Answer:

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