Use Fundamental Identities to Simplify the Expression Below and Then $\cos \alpha ( \sec \alpha - \cos \alpha )$

Multiple Choice

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

A) ​ $\frac { \csc ^ { 2 } \alpha - \sec ^ { 2 } \alpha + \tan ^ { 2 } \alpha } { \csc ^ { 2 } \alpha }$
B) ​ $1 - \sin ^ { 2 } \alpha$
C) ​ $\frac { \csc ^ { 2 } \alpha - 1 } { \csc ^ { 2 } \alpha }$
D) ​ $1 - \cos ^ { 2 } \alpha$
E) ​ $1 - \cot ^ { 2 } \alpha$