Multiply;then Use Fundamental Identities to Simplify the Expression Below and Determine

Multiple Choice

Multiply;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.​ $( \cot x + 1 ) ^ { 2 }$

A) ​ $\cot ^ { 2 } x + 1$
B) ​ $\cot ^ { 2 } x + 2 \cot x$
C) ​ $\cot ^ { 2 } x + 2 \cot x + 1$
D) ​ $\csc ^ { 2 } x ( 1 + 2 \sin x \cos x )$
E) ​ $\frac { 1 + 2 \sin x \cos x } { \sin ^ { 2 } x }$